diff --git a/pandas/core/base.py b/pandas/core/base.py
index fd039480fc6f1..9b50687edecd8 100644
--- a/pandas/core/base.py
+++ b/pandas/core/base.py
@@ -787,7 +787,36 @@ def empty(self):
         return not self.size
 
     def max(self):
-        """ The maximum value of the object """
+        """
+        Return the maximum value of the Index.
+
+        Returns
+        -------
+        scalar
+            Maximum value.
+
+        See Also
+        --------
+        Index.min : Return the minimum value in an Index.
+        Series.max : Return the maximum value in a Series.
+        DataFrame.max : Return the maximum values in a DataFrame.
+
+        Examples
+        --------
+        >>> idx = pd.Index([3, 2, 1])
+        >>> idx.max()
+        3
+
+        >>> idx = pd.Index(['c', 'b', 'a'])
+        >>> idx.max()
+        'c'
+
+        For a MultiIndex, the maximum is determined lexicographically.
+
+        >>> idx = pd.MultiIndex.from_product([('a', 'b'), (2, 1)])
+        >>> idx.max()
+        ('b', 2)
+        """
         return nanops.nanmax(self.values)
 
     def argmax(self, axis=None):