http://www.amazon.com/Data-Analysis-Bayesian-Tutorial-Public... is short and reputable on Bayesian statistics. On MCMC specifically, I don't know, but MCMC is really a kind of algorithm that lets you find the answer to a mathematical question (so I think understanding the math is the right thing to start with).
PS. There a second edition of that book, but I've heard that the first edition is better, because the second edition added a different author and expanded the book.
PS. There a second edition of that book, but I've heard that the first edition is better, because the second edition added a different author and expanded the book.