You can also use
git stash save -p "my commit message". This way you can select which hunks should be added to stash, whole files can be selected as well.
You'll be prompted with a few actions for each hunk:
y - stash this hunk n - do not stash this hunk q - quit; do not stash this hunk or any of the remaining ones a - stash this hunk and all later hunks in the file d - do not stash this hunk or any of the later hunks in the file g - select a hunk to go to / - search for a hunk matching the given regex j - leave this hunk undecided, see next undecided hunk J - leave this hunk undecided, see next hunk k - leave this hunk undecided, see previous undecided hunk K - leave this hunk undecided, see previous hunk s - split the current hunk into smaller hunks e - manually edit the current hunk ? - print help