Over the past 20 years, the study of superprocesses has expanded into a major industry and can now be regarded as a central theme in modern probability theory. This book is intended as a rapid introduction to the subject, geared toward graduate students and researchers in stochastic analysis. A variety of different approaches to the superprocesses emerged over the last ten years. Yet no one approach superseded any others. In this book, readers are exposed to a number of different ways of thinking about the processes, and each is used to motivate some key results. The emphasis is on why results are true rather than on rigorous proof. Specific results are given, including extensive references to current literature for their general form. Readership Graduate students and research mathematicians interested in probability and its applications. Reviews "The book is well written ... makes for joyful reading. The style is partially informal and aims more at an intuitive understanding than at technical proofs ... The book is thus very suitable for those who want rapid and comprehensive information and are ready to go back to the original works for technical details."  Translated from Jahresbericht der Deutschen MathematikerVereinigung Table of Contents  Superprocesses as diffusion approximations
 Qualitative behaviour I
 The Le Gall representation
 The relationship between our two classes of superprocesses
 A countable representation
 Qualitative behaviour II
 Introducing interactions
 Superprocesses and partial differential equations
 Some more interacting models
 Appendix
 Bibliography
 Index of notation
 Index
