What is kabbalah?

Kabbalah is an aspect of Jewish mysticism. It consists of a large body of speculation on the nature of divinity, the creation, the origin and fate of the soul, and the role of human beings. It consists also of meditative, devotional, mystical and magical practices which were taught only to a select few and for this reason Kabbalah is regarded as an esoteric offshoot of Judaism. Some aspects of Kabbalah have been studied and used by non-Jews for several hundred years.
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Kabbalah

To add to frankvan's reply kabbalah is considerad one of the most difficult aspects of judiasm to learn. The book the zohar, is a kabbalistk book, which many orthodox jews believe should not be learned until the age of fourty.
-yafa

Yes, Yafa, and I know forty-year-olds who still cannot find anyone to help them learn because they are still not old enough yet.

There is a book I highly recommend on that topic, Kabbalah: The Heart of Jewish Mysticism

I would recommend On the Kabbalah and Its Symbolism by Gershom Scholem, perhaps the most learned scholar on the subject.

For a taste of how it reads, "Zohar" is what I picked up. To add to Yafa's post, I was once told by a rabbi that in order to "qualify" to study, it's recommended that you be married and have two kids, that you've first mastered the Torah and the Talmud, and that you meet the age requirement. The recommendations were made with maturity in mind. The previous study for obvious reasons, to be well-rooted in fact and tradition before you attempt the more complex or abstract, and marriage/kids so that every day you'll return home to something that forces you to keep your feet on the ground.

You can see from the way the Occult has used Kaballah that it's not difficult to get carried away with numerology and other wierd stuff, even though the intent of the writers was obviously not "magic".