diff --git a/src/array_api_typing/__init__.py b/src/array_api_typing/__init__.py
index 3532743..f677768 100644
--- a/src/array_api_typing/__init__.py
+++ b/src/array_api_typing/__init__.py
@@ -1,10 +1,18 @@
 """Static typing support for the array API standard."""
 
 __all__ = (
+    "Array",
+    "ArrayNamespace",
+    "DType",
+    "Device",
     "HasArrayNamespace",
     "__version__",
     "__version_tuple__",
+    "signature_types",
 )
 
-from ._namespace import HasArrayNamespace
+from . import signature_types
+from ._array import Array
+from ._misc_objects import Device, DType
+from ._namespace import ArrayNamespace, HasArrayNamespace
 from ._version import version as __version__, version_tuple as __version_tuple__
diff --git a/src/array_api_typing/_array.py b/src/array_api_typing/_array.py
new file mode 100644
index 0000000..3677ae6
--- /dev/null
+++ b/src/array_api_typing/_array.py
@@ -0,0 +1,12 @@
+"""Static typing support for array API arrays."""
+
+from typing import Protocol
+
+from ._namespace import HasArrayNamespace
+
+
+class Array(HasArrayNamespace, Protocol):
+    """An Array API array of homogenously-typed numbers."""
+
+    # TODO(https://github.com/data-apis/array-api-typing/issues/23): Populate this
+    # protocol with methods defined by the Array API specification.
diff --git a/src/array_api_typing/_misc_objects.py b/src/array_api_typing/_misc_objects.py
new file mode 100644
index 0000000..061acc9
--- /dev/null
+++ b/src/array_api_typing/_misc_objects.py
@@ -0,0 +1,6 @@
+"""Static typing support for miscellaneous objects in the array API."""
+
+from typing import TypeAlias
+
+Device: TypeAlias = object  # The device on which an Array API array is stored.
+DType: TypeAlias = object  # The type of the numbers contained in an Array API array."""
diff --git a/src/array_api_typing/_namespace.py b/src/array_api_typing/_namespace.py
index 98099d1..0f31e61 100644
--- a/src/array_api_typing/_namespace.py
+++ b/src/array_api_typing/_namespace.py
@@ -1,13 +1,54 @@
 __all__ = ("HasArrayNamespace",)
 
-from types import ModuleType
-from typing import Protocol, final
+from __future__ import annotations
+
+from typing import TYPE_CHECKING, Protocol
 from typing_extensions import TypeVar
 
-T = TypeVar("T", bound=object, default=ModuleType)  # PEP 696 default
+if TYPE_CHECKING:
+    # This condition exists to prevent a circular import: _array imports _namespace for
+    # HasArrayNamespace. Therefore, _namespace cannot import _array except when
+    # type-checking. The type variable depends on Array, so we create a dummy type
+    # variable without the same bounds and default for this case.  In Python 3.13, this
+    # is no longer be necessary.
+    from typing_extensions import Buffer
+
+    from ._array import Array
+    from ._misc_objects import Device, DType
+    from .signature_types import NestedSequence
+
+    A = TypeVar("A", bound=Array, default=Array)  # PEP 696 default
+else:
+    A = TypeVar("A")
+
+
+class ArrayNamespace(Protocol[A]):
+    """An Array API namespace."""
+
+    def asarray(
+        self,
+        obj: Array | complex | NestedSequence[complex] | Buffer,
+        /,
+        *,
+        dtype: DType | None = None,
+        device: Device | None = None,
+        copy: bool | None = None,
+    ) -> A: ...
+
+    def astype(
+        self,
+        x: A,
+        dtype: DType,
+        /,
+        *,
+        copy: bool = True,
+        device: Device | None = None,
+    ) -> A: ...
+
+
+T = TypeVar("T", bound=ArrayNamespace, default=ArrayNamespace)  # PEP 696 default
 
 
-@final
 class HasArrayNamespace(Protocol[T]):  # type: ignore[misc]  # see python/mypy#17288
     """Protocol for classes that have an `__array_namespace__` method.
 
diff --git a/src/array_api_typing/signature_types/__init__.py b/src/array_api_typing/signature_types/__init__.py
new file mode 100644
index 0000000..52fff5a
--- /dev/null
+++ b/src/array_api_typing/signature_types/__init__.py
@@ -0,0 +1,7 @@
+"""Types that appear in public function signatures."""
+
+__all__ = [
+    "NestedSequence",
+]
+
+from ._signature_types import NestedSequence
diff --git a/src/array_api_typing/signature_types/_signature_types.py b/src/array_api_typing/signature_types/_signature_types.py
new file mode 100644
index 0000000..a6c91bc
--- /dev/null
+++ b/src/array_api_typing/signature_types/_signature_types.py
@@ -0,0 +1,77 @@
+from __future__ import annotations
+
+from typing import TYPE_CHECKING, Protocol, TypeVar, runtime_checkable
+
+if TYPE_CHECKING:
+    from collections.abc import Iterator
+
+_T_co = TypeVar("_T_co", covariant=True)
+
+
+@runtime_checkable
+class NestedSequence(Protocol[_T_co]):
+    """A protocol for representing nested sequences.
+
+    Warning:
+    -------
+    `NestedSequence` currently does not work in combination with type variables,
+    *e.g.* ``def func(a: NestedSequnce[T]) -> T: ...``.
+
+    See Also:
+    --------
+    collections.abc.Sequence:
+        ABCs for read-only and mutable :term:`sequences`.
+
+    Examples:
+    --------
+    .. code-block:: python
+
+        >>> from typing import TYPE_CHECKING
+        >>> import numpy as np
+        >>> import array_api_typing as xpt
+
+        >>> def get_dtype(seq: xpt.NestedSequence[float]) -> np.dtype[np.float64]:
+        ...     return np.asarray(seq).dtype
+
+        >>> a = get_dtype([1.0])
+        >>> b = get_dtype([[1.0]])
+        >>> c = get_dtype([[[1.0]]])
+        >>> d = get_dtype([[[[1.0]]]])
+
+        >>> if TYPE_CHECKING:
+        ...     reveal_locals()
+        ...     # note: Revealed local types are:
+        ...     # note:     a: numpy.dtype[numpy.floating[numpy._typing._64Bit]]
+        ...     # note:     b: numpy.dtype[numpy.floating[numpy._typing._64Bit]]
+        ...     # note:     c: numpy.dtype[numpy.floating[numpy._typing._64Bit]]
+        ...     # note:     d: numpy.dtype[numpy.floating[numpy._typing._64Bit]]
+
+    """
+
+    def __len__(self, /) -> int:
+        """Implement ``len(self)``."""
+        raise NotImplementedError
+
+    def __getitem__(self, index: int, /) -> _T_co | NestedSequence[_T_co]:
+        """Implement ``self[x]``."""
+        raise NotImplementedError
+
+    def __contains__(self, x: object, /) -> bool:
+        """Implement ``x in self``."""
+        raise NotImplementedError
+
+    def __iter__(self, /) -> Iterator[_T_co | NestedSequence[_T_co]]:
+        """Implement ``iter(self)``."""
+        raise NotImplementedError
+
+    def __reversed__(self, /) -> Iterator[_T_co | NestedSequence[_T_co]]:
+        """Implement ``reversed(self)``."""
+        raise NotImplementedError
+
+    def count(self, value: object, /) -> int:
+        """Return the number of occurrences of `value`."""
+        raise NotImplementedError
+
+    def index(self, value: object, /) -> int:
+        """Return the first index of `value`."""
+        raise NotImplementedError