Use the following git command to get a list of all the Moodle core git branches.
git ls-remote git://git.moodle.org/moodle.git | grep head
This returns a bunch of hashes and the
refs/heads/[MOODLE_XX_STABLE] branches. You can guess these, so this is just to check what they are without having to clone the entire repository. Plus you’ll know when a new stable branch is available in the repository.
To clone a specific branch (e.g. say I only want Moodle 2.2), use this command in the relevant target directory (note the -t to include tags so you can go to specific tags like v2.2.2):
git clone -b MOODLE_22_STABLE git://git.moodle.org/moodle.git