diff --git a/tianshou/data/batch.py b/tianshou/data/batch.py
index 5f84dfa..661fbe9 100644
--- a/tianshou/data/batch.py
+++ b/tianshou/data/batch.py
@@ -6,6 +6,7 @@
 from typing import (
     Any,
     Protocol,
+    Self,
     TypeVar,
     Union,
     cast,
@@ -232,7 +233,7 @@ def __getitem__(self, index: str) -> Any:
         ...
 
     @overload
-    def __getitem__(self: TBatch, index: IndexType) -> TBatch:
+    def __getitem__(self, index: IndexType) -> Self:
         ...
 
     def __getitem__(self, index: str | IndexType) -> Any:
@@ -241,22 +242,22 @@ def __getitem__(self, index: str | IndexType) -> Any:
     def __setitem__(self, index: str | IndexType, value: Any) -> None:
         ...
 
-    def __iadd__(self: TBatch, other: TBatch | Number | np.number) -> TBatch:
+    def __iadd__(self, other: Self | Number | np.number) -> Self:
         ...
 
-    def __add__(self: TBatch, other: TBatch | Number | np.number) -> TBatch:
+    def __add__(self, other: Self | Number | np.number) -> Self:
         ...
 
-    def __imul__(self: TBatch, value: Number | np.number) -> TBatch:
+    def __imul__(self, value: Number | np.number) -> Self:
         ...
 
-    def __mul__(self: TBatch, value: Number | np.number) -> TBatch:
+    def __mul__(self, value: Number | np.number) -> Self:
         ...
 
-    def __itruediv__(self: TBatch, value: Number | np.number) -> TBatch:
+    def __itruediv__(self, value: Number | np.number) -> Self:
         ...
 
-    def __truediv__(self: TBatch, value: Number | np.number) -> TBatch:
+    def __truediv__(self, value: Number | np.number) -> Self:
         ...
 
     def __repr__(self) -> str:
@@ -274,7 +275,7 @@ def to_torch(
         """Change all numpy.ndarray to torch.Tensor in-place."""
         ...
 
-    def cat_(self, batches: TBatch | Sequence[dict | TBatch]) -> None:
+    def cat_(self, batches: Self | Sequence[dict | Self]) -> None:
         """Concatenate a list of (or one) Batch objects into current batch."""
         ...
 
@@ -298,7 +299,7 @@ def cat(batches: Sequence[dict | TBatch]) -> TBatch:
         """
         ...
 
-    def stack_(self, batches: Sequence[dict | TBatch], axis: int = 0) -> None:
+    def stack_(self, batches: Sequence[dict | Self], axis: int = 0) -> None:
         """Stack a list of Batch object into current batch."""
         ...
 
@@ -327,7 +328,7 @@ def stack(batches: Sequence[dict | TBatch], axis: int = 0) -> TBatch:
         """
         ...
 
-    def empty_(self: TBatch, index: slice | IndexType | None = None) -> TBatch:
+    def empty_(self, index: slice | IndexType | None = None) -> Self:
         """Return an empty Batch object with 0 or None filled.
 
         If "index" is specified, it will only reset the specific indexed-data.
@@ -362,7 +363,7 @@ def empty(batch: TBatch, index: IndexType | None = None) -> TBatch:
         """
         ...
 
-    def update(self, batch: dict | TBatch | None = None, **kwargs: Any) -> None:
+    def update(self, batch: dict | Self | None = None, **kwargs: Any) -> None:
         """Update this batch from another dict/Batch."""
         ...
 
@@ -373,11 +374,11 @@ def is_empty(self, recurse: bool = False) -> bool:
         ...
 
     def split(
-        self: TBatch,
+        self,
         size: int,
         shuffle: bool = True,
         merge_last: bool = False,
-    ) -> Iterator[TBatch]:
+    ) -> Iterator[Self]:
         """Split whole data into multiple small batches.
 
         :param int size: divide the data batch with the given size, but one
@@ -457,7 +458,7 @@ def __getitem__(self, index: str) -> Any:
         ...
 
     @overload
-    def __getitem__(self: TBatch, index: IndexType) -> TBatch:
+    def __getitem__(self, index: IndexType) -> Self:
         ...
 
     def __getitem__(self, index: str | IndexType) -> Any:
@@ -501,7 +502,7 @@ def __setitem__(self, index: str | IndexType, value: Any) -> None:
                 else:
                     self.__dict__[key][index] = None
 
-    def __iadd__(self: TBatch, other: TBatch | Number | np.number) -> TBatch:
+    def __iadd__(self, other: Self | Number | np.number) -> Self:
         """Algebraic addition with another Batch instance in-place."""
         if isinstance(other, Batch):
             for (batch_key, obj), value in zip(
@@ -521,11 +522,11 @@ def __iadd__(self: TBatch, other: TBatch | Number | np.number) -> TBatch:
             return self
         raise TypeError("Only addition of Batch or number is supported.")
 
-    def __add__(self: TBatch, other: TBatch | Number | np.number) -> TBatch:
+    def __add__(self, other: Self | Number | np.number) -> Self:
         """Algebraic addition with another Batch instance out-of-place."""
         return deepcopy(self).__iadd__(other)
 
-    def __imul__(self: TBatch, value: Number | np.number) -> TBatch:
+    def __imul__(self, value: Number | np.number) -> Self:
         """Algebraic multiplication with a scalar value in-place."""
         assert _is_number(value), "Only multiplication by a number is supported."
         for batch_key, obj in self.__dict__.items():
@@ -534,11 +535,11 @@ def __imul__(self: TBatch, value: Number | np.number) -> TBatch:
             self.__dict__[batch_key] *= value
         return self
 
-    def __mul__(self: TBatch, value: Number | np.number) -> TBatch:
+    def __mul__(self, value: Number | np.number) -> Self:
         """Algebraic multiplication with a scalar value out-of-place."""
         return deepcopy(self).__imul__(value)
 
-    def __itruediv__(self: TBatch, value: Number | np.number) -> TBatch:
+    def __itruediv__(self, value: Number | np.number) -> Self:
         """Algebraic division with a scalar value in-place."""
         assert _is_number(value), "Only division by a number is supported."
         for batch_key, obj in self.__dict__.items():
@@ -547,7 +548,7 @@ def __itruediv__(self: TBatch, value: Number | np.number) -> TBatch:
             self.__dict__[batch_key] /= value
         return self
 
-    def __truediv__(self: TBatch, value: Number | np.number) -> TBatch:
+    def __truediv__(self, value: Number | np.number) -> Self:
         """Algebraic division with a scalar value out-of-place."""
         return deepcopy(self).__itruediv__(value)
 
@@ -604,7 +605,7 @@ def to_torch(
                     obj = obj.type(dtype)  # noqa: PLW2901
                 self.__dict__[batch_key] = obj
 
-    def __cat(self: TBatch, batches: Sequence[dict | TBatch], lens: list[int]) -> None:
+    def __cat(self, batches: Sequence[dict | Self], lens: list[int]) -> None:
         """Private method for Batch.cat_.
 
         ::
@@ -798,7 +799,7 @@ def stack(batches: Sequence[dict | TBatch], axis: int = 0) -> TBatch:
         # can't cast to a generic type, so we have to ignore the type here
         return batch  # type: ignore
 
-    def empty_(self: TBatch, index: slice | IndexType | None = None) -> TBatch:
+    def empty_(self, index: slice | IndexType | None = None) -> Self:
         for batch_key, obj in self.items():
             if isinstance(obj, torch.Tensor):  # most often case
                 self.__dict__[batch_key][index] = 0
@@ -826,7 +827,7 @@ def empty_(self: TBatch, index: slice | IndexType | None = None) -> TBatch:
     def empty(batch: TBatch, index: IndexType | None = None) -> TBatch:
         return deepcopy(batch).empty_(index)
 
-    def update(self, batch: dict | TBatch | None = None, **kwargs: Any) -> None:
+    def update(self, batch: dict | Self | None = None, **kwargs: Any) -> None:
         if batch is None:
             self.update(kwargs)
             return
@@ -902,11 +903,11 @@ def shape(self) -> list[int]:
         )
 
     def split(
-        self: TBatch,
+        self,
         size: int,
         shuffle: bool = True,
         merge_last: bool = False,
-    ) -> Iterator[TBatch]:
+    ) -> Iterator[Self]:
         length = len(self)
         if size == -1:
             size = length
diff --git a/tianshou/data/buffer/base.py b/tianshou/data/buffer/base.py
index 0a55300..3609b79 100644
--- a/tianshou/data/buffer/base.py
+++ b/tianshou/data/buffer/base.py
@@ -1,4 +1,4 @@
-from typing import Any, cast
+from typing import Any, Self, cast
 
 import h5py
 import numpy as np
@@ -111,7 +111,7 @@ def save_hdf5(self, path: str, compression: str | None = None) -> None:
             to_hdf5(self.__dict__, f, compression=compression)
 
     @classmethod
-    def load_hdf5(cls, path: str, device: str | None = None) -> "ReplayBuffer":
+    def load_hdf5(cls, path: str, device: str | None = None) -> Self:
         """Load replay buffer from HDF5 file."""
         with h5py.File(path, "r") as f:
             buf = cls.__new__(cls)
@@ -128,7 +128,7 @@ def from_data(
         truncated: h5py.Dataset,
         done: h5py.Dataset,
         obs_next: h5py.Dataset,
-    ) -> "ReplayBuffer":
+    ) -> Self:
         size = len(obs)
         assert all(
             len(dset) == size for dset in [obs, act, rew, terminated, truncated, done, obs_next]
diff --git a/tianshou/data/collector.py b/tianshou/data/collector.py
index fcf8653..7bca1db 100644
--- a/tianshou/data/collector.py
+++ b/tianshou/data/collector.py
@@ -62,13 +62,13 @@ def __init__(
         policy: BasePolicy,
         env: gym.Env | BaseVectorEnv,
         buffer: ReplayBuffer | None = None,
-        preprocess_fn: Callable[..., Batch] | None = None,
+        preprocess_fn: Callable[..., RolloutBatchProtocol] | None = None,
         exploration_noise: bool = False,
     ) -> None:
         super().__init__()
         if isinstance(env, gym.Env) and not hasattr(env, "__len__"):
             warnings.warn("Single environment detected, wrap to DummyVectorEnv.")
-            self.env = DummyVectorEnv([lambda: env])
+            self.env = DummyVectorEnv([lambda: env])  # type: ignore
         else:
             self.env = env  # type: ignore
         self.env_num = len(self.env)
@@ -413,7 +413,7 @@ def __init__(
         policy: BasePolicy,
         env: BaseVectorEnv,
         buffer: ReplayBuffer | None = None,
-        preprocess_fn: Callable[..., Batch] | None = None,
+        preprocess_fn: Callable[..., RolloutBatchProtocol] | None = None,
         exploration_noise: bool = False,
     ) -> None:
         # assert env.is_async
diff --git a/tianshou/env/utils.py b/tianshou/env/utils.py
index bc66321..b5be12f 100644
--- a/tianshou/env/utils.py
+++ b/tianshou/env/utils.py
@@ -1,4 +1,4 @@
-from typing import TYPE_CHECKING, Any, Union
+from typing import Any
 
 import cloudpickle
 import gymnasium
@@ -6,12 +6,7 @@
 
 from tianshou.env.pettingzoo_env import PettingZooEnv
 
-if TYPE_CHECKING:
-    import gym
-
-# TODO: remove gym entirely? Currently mypy complains in several places
-#  if gym.Env is removed from the Union
-ENV_TYPE = Union[gymnasium.Env, "gym.Env", PettingZooEnv]
+ENV_TYPE = gymnasium.Env | PettingZooEnv
 
 gym_new_venv_step_type = tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray, np.ndarray]
 
diff --git a/tianshou/policy/base.py b/tianshou/policy/base.py
index 44cef97..a779a76 100644
--- a/tianshou/policy/base.py
+++ b/tianshou/policy/base.py
@@ -11,7 +11,7 @@
 from torch import nn
 
 from tianshou.data import ReplayBuffer, to_numpy, to_torch_as
-from tianshou.data.batch import BatchProtocol, TBatch
+from tianshou.data.batch import BatchProtocol
 from tianshou.data.types import BatchWithReturnsProtocol, RolloutBatchProtocol
 from tianshou.utils import MultipleLRSchedulers
 
@@ -185,7 +185,7 @@ def forward(
         """
 
     @overload
-    def map_action(self, act: TBatch) -> TBatch:
+    def map_action(self, act: BatchProtocol) -> BatchProtocol:
         ...
 
     @overload