The web site for the course may be found here.
I am very happy that you are interested in taking physics 131. In the opinion of most theoretical physicists, including Einstein, general relativity is by far the most beautiful theory ever.
Several students have asked me about the requirement in the catalog of having taken physics 105b or taking it concurrently. As far as I am concerned, only you can judge if you ready for physics 131. I certainly do not want you to be unable to follow the course due to inadequate preparation. You and I will both be frustrated. I don't know what is covered in physics 105b, but as far as I am concerned, you should have the following.
(1) Prior exposure to special relativity: One issue in an undergraduate course on general relativity is how much time to devote to special relativity. I intend to spend the first week or so reviewing special relativity at a fairly fast pace such that there is no way you could really follow if you have never seen special relativity before. Ten weeks is an awfully short time and so I can't possibly spend more time on special relativity: I am sure that you would be unhappy if we get bogged down in special relativity and barely get to general relativity.
(2) Prior exposure to the variational principle in Newtonian mechanics: Specifically, you should be familiar with the material in section 3.5 of Hartle's book (see below).
Having said that, I would like to say that my own philosophy and my advice to physics students is to "stretch upward": take the most advanced courses you think you are ready for. But you MUST be prepared to work hard in this course. Einstein's gravity is definitely not for the casual tourist. You can't just sit back and admire Einstein's theory. Tourists are not allowed into this class. I will be using Hartle's book "Gravity: An Introduction to Einstein's General Relativity" and following it fairly closely. I would be foolish not to since the book is based on the author's 40 years of experience teaching here at UCSB. The course plan is described in the last sentence of the first paragraph D.3 on page 560. I have talked to Professor Hartle extensively about the course and his experience with UCSB undergraduates and he advised me to start with chapter 4. You are expected to have read chapters 1, 2, and 3.