This book details advanced techniques for investigating Brownian motion and continuous martingales. It serves as a comprehensive resource for probabilists, covering a wide array of calculations and theoretical developments. The text is structured to guide graduate students into research by presenting complex theories and further developments as exercises, encouraging active learning and exploration of open research questions.

The book is highly regarded, with one review calling it 'magnificent' and 'THE book for a capable graduate student starting out on research in probability.' Reviewers highlight its strength in presenting an enormous variety of calculations and theoretical developments, often embedded within exercises. The text is praised for its ability to guide readers through complex topics as if the authors were personally explaining them, while also pointing towards areas for future research. Successive editions have consistently incorporated significant advances in the field.