How do I move forward and backward between commits in git?

I've experimented a bit and this seems to do the trick to navigate forwards (edit: it works well only when you have a linear history without merge commits):

git checkout $(git rev-list --topo-order HEAD..towards | tail -1)

where towards is a SHA1 of the commit or a tag.

Explanation:

• the command inside $() means: get all the commits between current HEAD and towards commit (excluding HEAD), and sort them in the precedence order (like in git log by default -- instead of the chronological order which is weirdly the default for rev-list), and then take the last one (tail), i.e. the one we want to go to.
• this is evaluated in the subshell, and passed to git checkout to perform a checkout.

You can define a function accessible as a parameter-expecting alias in your .profile file to navigate forward towards the particular commit:

# Go forward in Git commit hierarchy, towards particular commit 
# Usage:
#  gofwd v1.2.7
# Does nothing when the parameter is not specified.
gofwd() {
  git checkout $(git rev-list --topo-order HEAD.."$*" | tail -1)
}

# Go back in Git commit hierarchy
# Usage: 
#  goback
alias goback='git checkout HEAD~'

I believe you can do:

git reset HEAD@{1}

To go one commit forward in time. To go forward multiple commits, use HEAD@{2}, HEAD@{3}, etc.

All you need to get clear, not detached head state is to reset, not checkout.

git reset HEAD@{1}