I'm taking an excellent course on Bayesian learning. The Dirichlet process has been one of the most interesting and challenging algorithms we've covered so I did some outside studying (this video lecture by Michael Jordan was especially helpful) and wrote a few notes which I'll share over the next few days, starting with this-

Click on the text to see it full size (I had to copy and paste screenshots to keep the formulas). Here's parts 1, 2, and 3 in pdf format instead, which may be easier to read.