In Normal Mode, . can be used to repeat your last action - although this only applies to editing actions (delete or paste) and not movements.
To undo something (again - edits, not movement), use u. In the original vi, this was a one-off, but in any current Vim version you can undo anything done in your current editing session.
The last lesson for the day is redo: Ctrl-r. Like undo, you can redo every undo done in this session.