How to diff a commit with its parent?

Use git show $COMMIT. It'll show you the log message for the commit, and the diff of that particular commit.

Use:

git diff 15dc8^!

as described in the following fragment of git-rev-parse(1) manpage (or in modern git gitrevisions(7) manpage):

Two other shorthands for naming a set that is formed by a commit and its parent commits exist. The r1^@ notation means all parents of r1. r1^! includes commit r1 but excludes all of its parents.

This means that you can use 15dc8^! as a shorthand for 15dc8^..15dc8 anywhere in git where revisions are needed. For diff command the git diff 15dc8^..15dc8 is understood as git diff 15dc8^ 15dc8, which means the difference between parent of commit (15dc8^) and commit (15dc8).

^{Note: the description in git-rev-parse(1) manpage talks about revision ranges, where it needs to work also for merge commits, with more than one parent. Then r1^! is "r1 --not r1^@" i.e. "r1 ^r1^1 ^r1^2 ..."}

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Also, you can use git show COMMIT to get commit description and diff for a commit. If you want only diff, you can use git diff-tree -p COMMIT

If you know how far back, you can try something like:

# Current branch vs. parent
git diff HEAD^ HEAD

# Current branch, diff between commits 2 and 3 times back
git diff HEAD~3 HEAD~2

Prior commits work something like this:

# Parent of HEAD
git show HEAD^1

# Grandparent
git show HEAD^2

There are a lot of ways you can specify commits:

# Great grandparent
git show HEAD~3

See this page for details.