Probability Theory (Courant Lecture Notes)

Covers most of the essentials concisely in less than 100 pages. Measure theory is not assumed as background, but prior exposure will help make the text seem less terse. Needs to supplemented with a more substantive text for examples, in which regard the book by Shiryaev makes an excellent companion.

This is an ideal text for first year graduate probability. Take Billingsley, which is several times bulkier, and distill the core concepts that one should away from the course, and that is Varadhan. Beautifully written, a joy to read, and occasionally even a useful reference to have on the desk to go back to when formalizing proofs for publication. For brevity's sake though, quite a few ideas have been left to exercises, and I am not sure if this is a text that an uninitiated can learn from without having the luxury of being in a class. These are course notes that Varadhan used to teach the course himself, so probably the intended audience is students taking a course - not self study.

The best foundational presentation of probability theory I have read. A minimalist approach that helps outfit the reader with tools to use in practice.

Very nice notes. This is very readable than other rigorous textbooks. I think this book is the best choice for review.

It's a little too concise...

I know which books I value when I end up buying a second copy after losing the first one. This book gives a complete overview of the basis of probability theory with some grounding in measure theory, and presents the main proofs. It is remarkable because of its concision and completeness: visibly prof Varadhan lectured from these notes and kept improving on them until we got this gem. There is not a single sentence too many, yet nothing is missing. For those who don't know who he is, Varadhan stands as one of the greatest probabilists of all time. Learning probability from him is like learning from Aristotle. Varadhan has two other similar volumes one covering stochastic processes the other into the theory of large deviations (though older than this current text). The book on Stochastic Processes should be paired with this one.

Varadhan is very succint, doesn't give too many details. I didn't use this book too much. My lecturer was Amir Dembo and his notes are pretty good (exact opposit of Varadhan - much longer and go over all details and more).