Beginner's guide to : Remove uncommitted changes in Git

Our case is, somewhat below :

(1) Remove changes on specific file.
(2) Remove all changes we made.

What we want is to get into the previous state, before we started to tinker with it.
We need to run this below for case (1) :

$ git checkout filename

And here below, to remove EVERY changes made :

$ git reset --hard HEAD || $ git reset --hard

(tips HEAD = last, HEAD^ = next to last, HEAD~2 = last - 2, and so on)