What are the differences between 'revert', 'amend,' 'rollback', and 'undo' a commit?

To help in my knowledge of git so I can use it day to day, what is the difference between:

• revert
• amend
• rollback
• undo

What are they and what do they do?

The terms revert and amend have a well-defined meaning in Git. In contrast, rollback and undo do not have such a well-defined meaning, and are open to interpretation.

Reverting a commit...

...means creating (on the current branch) a new commit that applies the inverse changes that another commit introduced. It's the preferred approach for correcting a problem in a repo that has already been shared with others, because it doesn't involve any destruction (i.e. rewriting history).

To revert a commit identified by <commit>, simply run

git revert <commit>

Amending a commit...

...means replacing the "current" commit by a new one that has the same parent(s); more details in How does git commit --amend work, exactly?

Be aware that

• amending a commit that you've already pushed to a shared remote is bad practice, because it's a form of history rewriting (it "deletes" the most recent commit, which your collaborators may have already based their work on);
• you can only amend the last commit on a given branch; to rewrite older commits, you need to bring out the big guns (e.g. interactive rebase).

To amend a commit, make all the required changes and stage them, then run

git commit --amend

No need to specify any commit, here, because the last commit on the current branch is the one that will be amended. Your editor will then pop up, giving you the opportunity to modify the commit message.

Rolling back...

...usually means discarding (or stashing) any local changes and resetting the branch to a commit (or simply checking out a commit, but that puts you in detached-HEAD state) prior to commit one where things started to get messed up. Use

git reset <commit-before-things-started-to-go-belly-up>

Undo a commit...

...can mean, depending on the context,

• revert a commit,
• amend a commit,
• remove a commit via an interactive rebase.