The purpose of the book is to bring together a large number of facts and formulas related to the Brownian movement. The handbook consists of two parts. The first part presents the general theory of diffusion and Brownian motion. The second part consists of tables containing more than 2550 explicit formulas for the distributions of functionals and their Laplace transformations for Brownian motion and related processes. The reference book can be useful to mathematicians, specialists in the field of financial mathematics, physicists and everyone who conducts applied research using to one degree or another the concepts of Brownian motion and diffusion. It can also be used for the educational process as a source of examples of probability distributions and explicit solutions to some differential problems.