From the reviews: "The author provides an excellent overview of methods from the theory of partial differential equations and stochastic processes used in mathematical finance. ... The book is well written, the mathematical level is quite sophisticated and a broad range of material is covered. At the same time, there is a clear focus on applications. The book is therefore warmly recommended for graduate students as well as for professionals in the financial industry." (Johan Tysk, Mathematical Reviews, Issue 2012 i) "The book is written for graduate and advanced undergraduate students and gives an introduction to the modern theory of option pricing. ... this book covers a wide range of topics with good motivations on a rigorous mathematical level." (Soren Christensen, Zentralblatt MATH, Vol. 1214, 2011)