As far as beginning graduate-level books on probability are concerned this is definitely one of the best. This looks like a set of lectures turned into a book.
The competition in my mind would be
First Look at Rigorous Probability Theory (more compact, perhaps a little dense)
Probability & Measure Theory, Second Edition (covers more ground and is very clear)
A Course in Probability Theory, Revised Edition, Second Edition(very detailed explanations, but you should probably have followed a course on measure theory)

Please dont dive into probability at this level, your intuition might not be ready for it.
To do that I recommend
An Introduction to Probability Theory and Its Applications, Vol. 1 (Volume 1) (if you have the time)
There is also Basic Probability Theory (Dover Books on Mathematics) which is an excellent introduction stopping short of measure theory.

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