diff --git a/src/hamcrest/core/core/isinstanceof.py b/src/hamcrest/core/core/isinstanceof.py
index a34aaa6..b234ca6 100644
--- a/src/hamcrest/core/core/isinstanceof.py
+++ b/src/hamcrest/core/core/isinstanceof.py
@@ -1,4 +1,4 @@
-from typing import Type
+from typing import Type, Any
 
 from hamcrest.core.base_matcher import BaseMatcher
 from hamcrest.core.description import Description
@@ -23,7 +23,7 @@ def describe_to(self, description: Description) -> None:
         description.append_text("an instance of ").append_text(self.expected_type.__name__)
 
 
-def instance_of(atype: Type) -> Matcher[object]:
+def instance_of(atype: Type[Any]) -> Matcher[object]:
     """Matches if object is an instance of, or inherits from, a given type.
 
     :param atype: The type to compare against as the expected type.
diff --git a/src/hamcrest/core/core/raises.py b/src/hamcrest/core/core/raises.py
index 0fcd6fe..c62bc0c 100644
--- a/src/hamcrest/core/core/raises.py
+++ b/src/hamcrest/core/core/raises.py
@@ -88,7 +88,9 @@ def describe_match(self, item, match_description: Description) -> None:
         )
 
 
-def raises(exception: Type[Exception], pattern=None, matching=None) -> Matcher[Callable[..., Any]]:
+def raises(
+    exception: Type[Exception], pattern: Optional[str] = None, matching: Optional[Matcher] = None
+) -> Matcher[Callable[..., Any]]:
     """Matches if the called function raised the expected exception.
 
     :param exception:  The class of the expected exception
@@ -121,7 +123,7 @@ def __init__(self, func: Callable[..., Any]):
     def __call__(self):
         self.func(*self.args, **self.kwargs)
 
-    def with_args(self, *args, **kwargs):
+    def with_args(self, *args: Any, **kwargs: Any):
         self.args = args
         self.kwargs = kwargs
         return self