Surveying a wide variety of mathematical models of diffusion in the ecological context, this book is written with the primary intent of providing scientists, particularly physicists but also biologists, with some background of the mathematics and physics of diffusion and how they can be applied to ecological problems. Equally, this is a specialized text book for graduates interested in mathematical ecology -- assuming no more than a basic knowledge of probability and differential equations. Each chapter in this new edition has been substantially updated by appopriate leading researchers in the field and contains much new material covering recent developments.