Besides Witchcraft, what other types of magic are there?

Magic can (arguably) be generally divided into 4 categories. Witchcraft, Sorcery, Shamanism and Alchemy. Alli of these involve the manipulation of energy, but differ in how it is accomplished. Witches cast spells which involves releasing their own energy "coded" for their intention into the Universe. Sorcerers summon spirits, demons, daemons or other energetic (spiritual) entities and compel them to accomplish the task for them. Shamans engage in Astral Projection. They leave their bodies and go out into the Universe to accomplish the task "manually" and convince spirits, usually by establishing friendly relationships with them, to assist in accomplishing their desired ends. Alchemists research the energy contained within natural objects, plants, stones, chemicals, elementsi, etc. and combine those objects to make potions or charms (or even meals) so that the energy from the finished product- once ingested or worn, will draw something to the user or send something away from him or her.

Most magic-users do not stick to just one technique. Most people who claim Shamanism as their magical path also employ Alchemy and sometimes Witchcraft. Many Witches employ Alchemy (especially Kitchen Witches) and Shamanism as well.