Stroock in the preface to his preface gives his graduate school introduction to probability from Kac and McKean to explain why the book is written from the analytic rather than the probabilistic viewpoint. The coverage is thorough and rigorous with important proofs provided in the style he likes best. As an example in Chapter 2 where he covers the central limit theorem and the Berry-Esseen results on rates of convergence, he uses Stein's method rather than more complicated approaches using Fourier series.

This covers all the standard topics for a first year graduate course in probability and a bit more.