How to programmatically switch between vertex, edge and face selection mode

Change the mesh_select_mode property to switch in mesh edit mode between vertex, edge and polygon selection mode in Blender.

For vertex selection mode:

Edge selection mode:

And face selection mode:

The multi-select mode is enabled too. For example for vertex and face selection mode:

In BMesh for vertex, edge and face selection mode:

For multi-select in BMesh: