Referring to the previous/next commit in git?
To simply answer the question from title (since that's what got me here from Google):
To checkout the previous commit:
git checkout HEAD^
To checkout the next commit (assuming there's no branching):
git checkout `git log --reverse --ancestry-path HEAD..master | head -n 1 | cut -d \ -f 2`
To refer to most recent commit on the branch you can also use @~1
git checkout @~1
You have a very clear explanation of how this works in the chapter on Acenstry References in Pro Git:
~is used to get the first parent.^can be used to get the other parents (^2, for example, for a merge).
But you don't have a simple way to reference the next commit, even if there are more convoluted ways to get it.
Inspired by @cexbrayat's answer, I find it useful to think of it this way:
How to refer to something in a commit's ancestry, where a commit can have multiple parents:
^nspecifies which parent~nspecifies which generation
Both default to one.