Dr Daniel W. Stroock is the Simons Professor of Mathematics Emeritus at the Massachusetts Institute of Technology. He has published numerous articles and is the author of six books, most recently Probability Theory: An Analytic View, 2nd edition (2010).

• 1. Kolmogorov's forward, basic results; 2. Non-elliptic regularity results; 3. Preliminary elliptic regularity results; 4. Nash theory; 5. Localization; 6. On a manifold; 7. Subelliptic estimates and Hörmander's theorem.

'The book will capture your attention with elegant proofs presented in an almost perfectly self-contained manner, with abundant talk in a lecturer's tone by the author himself, but with a little bit of an aficionado's taste. The book, arranged idiosyncratically, has such a strong impact that, at the next moment, you may find yourself carried away in looking for mathematical treasures scattered here and there in each chapter. The reviewer recommends the present book with confidence to anyone who in interested in PDE and probability theory. At least you should always keep this at your side if you are a probabilist at all.' Isamu Doku, Mathematical Reviews