In Edit Mode, in the 3D View, is there a hotkey for toggling between vertex/edge/face editing?
From Blender 2.8 on wards, there are the following hot keys while in Edit Mode:
1 for Vertex select
2 for Edge select
3 for Face select
You can add multiple active modes by holding Shift while pressing one of the 3 keys, allowing to activate all 3 at once if so desired.
Holding Ctrl on the other hand, when pressing 2 for example would limit the selection mode to the edge selection again, regardless which selection mode(s) was/were selected before.
Other then the direct hotkeys (not sure why the specific hotkeys are not shown), the information regarding the use of Shift and Ctrl can also be found by hovering over the icon for the selection modes.
This is based on the default installation of Blender 2.8+ addons can and have changed those hotkeys.
Should there be an issue with the default hotkeys, it's recommended to first go in the Blender Preferences and look under Keymap and search for 1.
In the Mesh section we find the Edit Mode related hotkeys:
marked red the important parts for in this case the vertex selection key-bind