This course will follow the textbook:

  • Buy at Amazon Durrett, Rick. Probability: Theory and Examples. 4th ed. Cambridge University Press, 2010. ISBN: 9780521765398. [Preview with Google Books]

I use the same notation as Durrett whenever possible.

In addition to the main textbook, there are many excellent textbooks and sets of lecture notes that cover the material of this course, several written by people right here at MIT. The course material is contained in the union of the following online texts for first-year graduate probability courses:

A gentler introduction to some of the material in the course appears in David Gamarnik's notes. For a more general analysis reference, there is also the online text Applied Analysis by Hunter and Nachtergaele.

Other excellent graduate probability books (that I don't think have been posted online, at least not by the authors) include (but are obviously not limited to):

  • Buy at Amazon Billingsley, Patrick. Probability and Measure. Anniv. ed. Wiley, 2012. ISBN: 9781118122372. [Preview with Google Books]
  • Buy at Amazon Dudley, R. M. Real Analysis and Probability. Cambridge University Press, 2002. ISBN: 9780521007542. [Preview with Google Books]
  • Buy at Amazon Stroock, Daniel. Probability Theory: An Analytic View. 2nd ed. Cambridge University Press, 2010. ISBN: 9780431087023. [Preview with Google Books]
  • Buy at Amazon Williams, David. Probability with Martingales. China Press, 2008. ISBN: 9787506292511.

There's a lot of overlap between these books, but you'll develop strong opinions if you spend much time with them. Here is one person's rated list of graduate probability books. (You probably won't agree with the list author's opinions, but it's still a nice list.)