diff --git a/pandas/util/_decorators.py b/pandas/util/_decorators.py
index 2e91d76b0fe98..d10d3a1f71fe6 100644
--- a/pandas/util/_decorators.py
+++ b/pandas/util/_decorators.py
@@ -294,7 +294,6 @@ def update(self, *args, **kwargs) -> None:
         """
         Update self.params with supplied args.
         """
-
         if isinstance(self.params, dict):
             self.params.update(*args, **kwargs)
 
diff --git a/pandas/util/_depr_module.py b/pandas/util/_depr_module.py
index 99dafdd760d26..5733663dd7ab3 100644
--- a/pandas/util/_depr_module.py
+++ b/pandas/util/_depr_module.py
@@ -4,11 +4,13 @@
 """
 
 import importlib
+from typing import Iterable
 import warnings
 
 
 class _DeprecatedModule:
-    """ Class for mocking deprecated modules.
+    """
+    Class for mocking deprecated modules.
 
     Parameters
     ----------
@@ -34,7 +36,7 @@ def __init__(self, deprmod, deprmodto=None, removals=None, moved=None):
         # For introspection purposes.
         self.self_dir = frozenset(dir(type(self)))
 
-    def __dir__(self):
+    def __dir__(self) -> Iterable[str]:
         deprmodule = self._import_deprmod()
         return dir(deprmodule)
 
diff --git a/pandas/util/_doctools.py b/pandas/util/_doctools.py
index 91972fed7a3bb..8fd4566d7763b 100644
--- a/pandas/util/_doctools.py
+++ b/pandas/util/_doctools.py
@@ -1,3 +1,5 @@
+from typing import Optional, Tuple
+
 import numpy as np
 
 import pandas as pd
@@ -9,24 +11,27 @@ class TablePlotter:
     Used in merging.rst
     """
 
-    def __init__(self, cell_width=0.37, cell_height=0.25, font_size=7.5):
+    def __init__(
+        self,
+        cell_width: float = 0.37,
+        cell_height: float = 0.25,
+        font_size: float = 7.5,
+    ):
         self.cell_width = cell_width
         self.cell_height = cell_height
         self.font_size = font_size
 
-    def _shape(self, df):
+    def _shape(self, df: pd.DataFrame) -> Tuple[int, int]:
         """
         Calculate table chape considering index levels.
         """
-
         row, col = df.shape
         return row + df.columns.nlevels, col + df.index.nlevels
 
-    def _get_cells(self, left, right, vertical):
+    def _get_cells(self, left, right, vertical) -> Tuple[int, int]:
         """
         Calculate appropriate figure size based on left and right data.
         """
-
         if vertical:
             # calculate required number of cells
             vcells = max(sum(self._shape(l)[0] for l in left), self._shape(right)[0])
@@ -36,7 +41,7 @@ def _get_cells(self, left, right, vertical):
             hcells = sum([self._shape(l)[1] for l in left] + [self._shape(right)[1]])
         return hcells, vcells
 
-    def plot(self, left, right, labels=None, vertical=True):
+    def plot(self, left, right, labels=None, vertical: bool = True):
         """
         Plot left / right DataFrames in specified layout.
 
@@ -45,7 +50,7 @@ def plot(self, left, right, labels=None, vertical=True):
         left : list of DataFrames before operation is applied
         right : DataFrame of operation result
         labels : list of str to be drawn as titles of left DataFrames
-        vertical : bool
+        vertical : bool, default True
             If True, use vertical layout. If False, use horizontal layout.
         """
         import matplotlib.pyplot as plt
@@ -96,7 +101,9 @@ def plot(self, left, right, labels=None, vertical=True):
         return fig
 
     def _conv(self, data):
-        """Convert each input to appropriate for table outplot"""
+        """
+        Convert each input to appropriate for table outplot.
+        """
         if isinstance(data, pd.Series):
             if data.name is None:
                 data = data.to_frame(name="")
@@ -127,7 +134,7 @@ def _insert_index(self, data):
             data.columns = col
         return data
 
-    def _make_table(self, ax, df, title, height=None):
+    def _make_table(self, ax, df, title: str, height: Optional[float] = None):
         if df is None:
             ax.set_visible(False)
             return
diff --git a/pandas/util/_exceptions.py b/pandas/util/_exceptions.py
index b8719154eb791..0723a37b1ba82 100644
--- a/pandas/util/_exceptions.py
+++ b/pandas/util/_exceptions.py
@@ -4,7 +4,9 @@
 
 @contextlib.contextmanager
 def rewrite_exception(old_name: str, new_name: str):
-    """Rewrite the message of an exception."""
+    """
+    Rewrite the message of an exception.
+    """
     try:
         yield
     except Exception as err:
diff --git a/pandas/util/_print_versions.py b/pandas/util/_print_versions.py
index b9f7e0c69f8b6..2801a2bf9c371 100644
--- a/pandas/util/_print_versions.py
+++ b/pandas/util/_print_versions.py
@@ -12,8 +12,9 @@
 
 
 def get_sys_info() -> List[Tuple[str, Optional[Union[str, int]]]]:
-    "Returns system information as a list"
-
+    """
+    Returns system information as a list
+    """
     blob: List[Tuple[str, Optional[Union[str, int]]]] = []
 
     # get full commit hash
@@ -123,7 +124,7 @@ def show_versions(as_json=False):
             print(tpl.format(k=k, stat=stat))
 
 
-def main():
+def main() -> int:
     from optparse import OptionParser
 
     parser = OptionParser()
diff --git a/pandas/util/_test_decorators.py b/pandas/util/_test_decorators.py
index 0e3ea25bf6fdb..7e14ed27d5bd4 100644
--- a/pandas/util/_test_decorators.py
+++ b/pandas/util/_test_decorators.py
@@ -37,7 +37,7 @@ def test_foo():
 from pandas.core.computation.expressions import _NUMEXPR_INSTALLED, _USE_NUMEXPR
 
 
-def safe_import(mod_name, min_version=None):
+def safe_import(mod_name: str, min_version: Optional[str] = None):
     """
     Parameters:
     -----------
@@ -110,7 +110,7 @@ def _skip_if_not_us_locale():
         return True
 
 
-def _skip_if_no_scipy():
+def _skip_if_no_scipy() -> bool:
     return not (
         safe_import("scipy.stats")
         and safe_import("scipy.sparse")
@@ -195,7 +195,9 @@ def skip_if_no(package: str, min_version: Optional[str] = None) -> Callable:
 )
 
 
-def skip_if_np_lt(ver_str, reason=None, *args, **kwds):
+def skip_if_np_lt(
+    ver_str: str, reason: Optional[str] = None, *args, **kwds
+) -> Callable:
     if reason is None:
         reason = f"NumPy {ver_str} or greater required"
     return pytest.mark.skipif(
@@ -211,14 +213,14 @@ def parametrize_fixture_doc(*args):
     initial fixture docstring by replacing placeholders {0}, {1} etc
     with parameters passed as arguments.
 
-    Parameters:
+    Parameters
     ----------
-        args: iterable
-            Positional arguments for docstring.
+    args: iterable
+        Positional arguments for docstring.
 
-    Returns:
+    Returns
     -------
-    documented_fixture: function
+    function
         The decorated function wrapped within a pytest
         ``parametrize_fixture_doc`` mark
     """
@@ -230,7 +232,7 @@ def documented_fixture(fixture):
     return documented_fixture
 
 
-def check_file_leaks(func):
+def check_file_leaks(func) -> Callable:
     """
     Decorate a test function tot check that we are not leaking file descriptors.
     """
diff --git a/pandas/util/_tester.py b/pandas/util/_tester.py
index 6a3943cab692e..b299f3790ab22 100644
--- a/pandas/util/_tester.py
+++ b/pandas/util/_tester.py
@@ -1,5 +1,5 @@
 """
-Entrypoint for testing from the top-level namespace
+Entrypoint for testing from the top-level namespace.
 """
 import os
 import sys
@@ -22,7 +22,8 @@ def test(extra_args=None):
             extra_args = [extra_args]
         cmd = extra_args
     cmd += [PKG]
-    print(f"running: pytest {' '.join(cmd)}")
+    joined = " ".join(cmd)
+    print(f"running: pytest {joined}")
     sys.exit(pytest.main(cmd))
 
 
diff --git a/pandas/util/_validators.py b/pandas/util/_validators.py
index 8b675a6b688fe..547fe748ae941 100644
--- a/pandas/util/_validators.py
+++ b/pandas/util/_validators.py
@@ -15,7 +15,6 @@ def _check_arg_length(fname, args, max_fname_arg_count, compat_args):
     Checks whether 'args' has length of at most 'compat_args'. Raises
     a TypeError if that is not the case, similar to in Python when a
     function is called with too many arguments.
-
     """
     if max_fname_arg_count < 0:
         raise ValueError("'max_fname_arg_count' must be non-negative")
@@ -38,7 +37,6 @@ def _check_for_default_values(fname, arg_val_dict, compat_args):
 
     Note that this function is to be called only when it has been
     checked that arg_val_dict.keys() is a subset of compat_args
-
     """
     for key in arg_val_dict:
         # try checking equality directly with '=' operator,
@@ -65,11 +63,8 @@ def _check_for_default_values(fname, arg_val_dict, compat_args):
 
         if not match:
             raise ValueError(
-                (
-                    f"the '{key}' parameter is not "
-                    "supported in the pandas "
-                    f"implementation of {fname}()"
-                )
+                f"the '{key}' parameter is not supported in "
+                f"the pandas implementation of {fname}()"
             )
 
 
@@ -79,19 +74,18 @@ def validate_args(fname, args, max_fname_arg_count, compat_args):
     has at most `len(compat_args)` arguments and whether or not all of these
     elements in `args` are set to their default values.
 
-    fname: str
+    Parameters
+    ----------
+    fname : str
         The name of the function being passed the `*args` parameter
-
-    args: tuple
+    args : tuple
         The `*args` parameter passed into a function
-
-    max_fname_arg_count: int
+    max_fname_arg_count : int
         The maximum number of arguments that the function `fname`
         can accept, excluding those in `args`. Used for displaying
         appropriate error messages. Must be non-negative.
-
-    compat_args: OrderedDict
-        A ordered dictionary of keys and their associated default values.
+    compat_args : Dict
+        An ordered dictionary of keys and their associated default values.
         In order to accommodate buggy behaviour in some versions of `numpy`,
         where a signature displayed keyword arguments but then passed those
         arguments **positionally** internally when calling downstream
@@ -101,10 +95,11 @@ def validate_args(fname, args, max_fname_arg_count, compat_args):
 
     Raises
     ------
-    TypeError if `args` contains more values than there are `compat_args`
-    ValueError if `args` contains values that do not correspond to those
-    of the default values specified in `compat_args`
-
+    TypeError
+        If `args` contains more values than there are `compat_args`
+    ValueError
+        If `args` contains values that do not correspond to those
+        of the default values specified in `compat_args`
     """
     _check_arg_length(fname, args, max_fname_arg_count, compat_args)
 
@@ -119,7 +114,6 @@ def _check_for_invalid_keys(fname, kwargs, compat_args):
     """
     Checks whether 'kwargs' contains any keys that are not
     in 'compat_args' and raises a TypeError if there is one.
-
     """
     # set(dict) --> set of the dictionary's keys
     diff = set(kwargs) - set(compat_args)
@@ -139,12 +133,10 @@ def validate_kwargs(fname, kwargs, compat_args):
 
     Parameters
     ----------
-    fname: str
+    fname : str
         The name of the function being passed the `**kwargs` parameter
-
-    kwargs: dict
+    kwargs : dict
         The `**kwargs` parameter passed into `fname`
-
     compat_args: dict
         A dictionary of keys that `kwargs` is allowed to have and their
         associated default values
@@ -154,7 +146,6 @@ def validate_kwargs(fname, kwargs, compat_args):
     TypeError if `kwargs` contains keys not in `compat_args`
     ValueError if `kwargs` contains keys in `compat_args` that do not
     map to the default values specified in `compat_args`
-
     """
     kwds = kwargs.copy()
     _check_for_invalid_keys(fname, kwargs, compat_args)
@@ -171,18 +162,14 @@ def validate_args_and_kwargs(fname, args, kwargs, max_fname_arg_count, compat_ar
     ----------
     fname: str
         The name of the function being passed the `**kwargs` parameter
-
     args: tuple
         The `*args` parameter passed into a function
-
     kwargs: dict
         The `**kwargs` parameter passed into `fname`
-
     max_fname_arg_count: int
         The minimum number of arguments that the function `fname`
         requires, excluding those in `args`. Used for displaying
         appropriate error messages. Must be non-negative.
-
     compat_args: OrderedDict
         A ordered dictionary of keys that `kwargs` is allowed to
         have and their associated default values. Note that if there
diff --git a/pandas/util/testing.py b/pandas/util/testing.py
index 6350b1075f4a0..c31cddc102afb 100644
--- a/pandas/util/testing.py
+++ b/pandas/util/testing.py
@@ -8,7 +8,7 @@
 from shutil import rmtree
 import string
 import tempfile
-from typing import Union, cast
+from typing import List, Optional, Union, cast
 import warnings
 import zipfile
 
@@ -22,6 +22,7 @@
 )
 
 import pandas._libs.testing as _testing
+from pandas._typing import FrameOrSeries
 from pandas.compat import _get_lzma_file, _import_lzma
 
 from pandas.core.dtypes.common import (
@@ -97,11 +98,10 @@ def reset_display_options():
     """
     Reset the display options for printing and representing objects.
     """
-
     pd.reset_option("^display.", silent=True)
 
 
-def round_trip_pickle(obj, path=None):
+def round_trip_pickle(obj: FrameOrSeries, path: Optional[str] = None) -> FrameOrSeries:
     """
     Pickle an object and then read it again.
 
@@ -114,10 +114,9 @@ def round_trip_pickle(obj, path=None):
 
     Returns
     -------
-    round_trip_pickled_object : pandas object
+    pandas object
         The original object that was pickled and then re-read.
     """
-
     if path is None:
         path = f"__{rands(10)}__.pickle"
     with ensure_clean(path) as path:
@@ -125,7 +124,7 @@ def round_trip_pickle(obj, path=None):
         return pd.read_pickle(path)
 
 
-def round_trip_pathlib(writer, reader, path=None):
+def round_trip_pathlib(writer, reader, path: Optional[str] = None):
     """
     Write an object to file specified by a pathlib.Path and read it back
 
@@ -140,10 +139,9 @@ def round_trip_pathlib(writer, reader, path=None):
 
     Returns
     -------
-    round_trip_object : pandas object
+    pandas object
         The original object that was serialized and then re-read.
     """
-
     import pytest
 
     Path = pytest.importorskip("pathlib").Path
@@ -155,9 +153,9 @@ def round_trip_pathlib(writer, reader, path=None):
     return obj
 
 
-def round_trip_localpath(writer, reader, path=None):
+def round_trip_localpath(writer, reader, path: Optional[str] = None):
     """
-    Write an object to file specified by a py.path LocalPath and read it back
+    Write an object to file specified by a py.path LocalPath and read it back.
 
     Parameters
     ----------
@@ -170,7 +168,7 @@ def round_trip_localpath(writer, reader, path=None):
 
     Returns
     -------
-    round_trip_object : pandas object
+    pandas object
         The original object that was serialized and then re-read.
     """
     import pytest
@@ -187,21 +185,20 @@ def round_trip_localpath(writer, reader, path=None):
 @contextmanager
 def decompress_file(path, compression):
     """
-    Open a compressed file and return a file object
+    Open a compressed file and return a file object.
 
     Parameters
     ----------
     path : str
-        The path where the file is read from
+        The path where the file is read from.
 
     compression : {'gzip', 'bz2', 'zip', 'xz', None}
         Name of the decompression to use
 
     Returns
     -------
-    f : file object
+    file object
     """
-
     if compression is None:
         f = open(path, "rb")
     elif compression == "gzip":
@@ -247,7 +244,6 @@ def write_to_compressed(compression, path, data, dest="test"):
     ------
     ValueError : An invalid compression value was passed in.
     """
-
     if compression == "zip":
         import zipfile
 
@@ -279,7 +275,11 @@ def write_to_compressed(compression, path, data, dest="test"):
 
 
 def assert_almost_equal(
-    left, right, check_dtype="equiv", check_less_precise=False, **kwargs
+    left,
+    right,
+    check_dtype: Union[bool, str] = "equiv",
+    check_less_precise: Union[bool, int] = False,
+    **kwargs,
 ):
     """
     Check that the left and right objects are approximately equal.
@@ -306,7 +306,6 @@ def assert_almost_equal(
         compare the **ratio** of the second number to the first number and
         check whether it is equivalent to 1 within the specified precision.
     """
-
     if isinstance(left, pd.Index):
         assert_index_equal(
             left,
@@ -389,13 +388,13 @@ def _check_isinstance(left, right, cls):
         )
 
 
-def assert_dict_equal(left, right, compare_keys=True):
+def assert_dict_equal(left, right, compare_keys: bool = True):
 
     _check_isinstance(left, right, dict)
     _testing.assert_dict_equal(left, right, compare_keys=compare_keys)
 
 
-def randbool(size=(), p=0.5):
+def randbool(size=(), p: float = 0.5):
     return rand(*size) <= p
 
 
@@ -407,7 +406,9 @@ def randbool(size=(), p=0.5):
 
 
 def rands_array(nchars, size, dtype="O"):
-    """Generate an array of byte strings."""
+    """
+    Generate an array of byte strings.
+    """
     retval = (
         np.random.choice(RANDS_CHARS, size=nchars * np.prod(size))
         .view((np.str_, nchars))
@@ -420,7 +421,9 @@ def rands_array(nchars, size, dtype="O"):
 
 
 def randu_array(nchars, size, dtype="O"):
-    """Generate an array of unicode strings."""
+    """
+    Generate an array of unicode strings.
+    """
     retval = (
         np.random.choice(RANDU_CHARS, size=nchars * np.prod(size))
         .view((np.unicode_, nchars))
@@ -468,7 +471,8 @@ def close(fignum=None):
 
 @contextmanager
 def ensure_clean(filename=None, return_filelike=False):
-    """Gets a temporary path and agrees to remove on close.
+    """
+    Gets a temporary path and agrees to remove on close.
 
     Parameters
     ----------
@@ -553,8 +557,9 @@ def ensure_safe_environment_variables():
 # Comparators
 
 
-def equalContents(arr1, arr2):
-    """Checks if the set of unique elements of arr1 and arr2 are equivalent.
+def equalContents(arr1, arr2) -> bool:
+    """
+    Checks if the set of unique elements of arr1 and arr2 are equivalent.
     """
     return frozenset(arr1) == frozenset(arr2)
 
@@ -691,8 +696,10 @@ def _get_ilevel_values(index, level):
             assert_categorical_equal(left.values, right.values, obj=f"{obj} category")
 
 
-def assert_class_equal(left, right, exact=True, obj="Input"):
-    """checks classes are equal."""
+def assert_class_equal(left, right, exact: Union[bool, str] = True, obj="Input"):
+    """
+    Checks classes are equal.
+    """
     __tracebackhide__ = True
 
     def repr_class(x):
@@ -2641,8 +2648,9 @@ def _constructor(self):
 
 
 @contextmanager
-def set_timezone(tz):
-    """Context manager for temporarily setting a timezone.
+def set_timezone(tz: str):
+    """
+    Context manager for temporarily setting a timezone.
 
     Parameters
     ----------
@@ -2685,7 +2693,8 @@ def setTZ(tz):
 
 
 def _make_skipna_wrapper(alternative, skipna_alternative=None):
-    """Create a function for calling on an array.
+    """
+    Create a function for calling on an array.
 
     Parameters
     ----------
@@ -2697,7 +2706,7 @@ def _make_skipna_wrapper(alternative, skipna_alternative=None):
 
     Returns
     -------
-    skipna_wrapper : function
+    function
     """
     if skipna_alternative:
 
@@ -2715,7 +2724,7 @@ def skipna_wrapper(x):
     return skipna_wrapper
 
 
-def convert_rows_list_to_csv_str(rows_list):
+def convert_rows_list_to_csv_str(rows_list: List[str]):
     """
     Convert list of CSV rows to single CSV-formatted string for current OS.
 
@@ -2723,13 +2732,13 @@ def convert_rows_list_to_csv_str(rows_list):
 
     Parameters
     ----------
-    rows_list : list
-        The list of string. Each element represents the row of csv.
+    rows_list : List[str]
+        Each element represents the row of csv.
 
     Returns
     -------
-    expected : string
-        Expected output of to_csv() in current OS
+    str
+        Expected output of to_csv() in current OS.
     """
     sep = os.linesep
     expected = sep.join(rows_list) + sep