A compact and rigorous treatment of measure-valued branching processes and immigration processes is given in the book at the level readable for graduate students. For the convenience of references, special attention has been paid to the generality of the framework. To develop a reasonably rich theory, the basic regularities of the models are certainly necessary.

In the first part of the book, the author not only constructs the transition semigroups of superprocesses with general spatial motions and branching mechanisms, but also proves the existence of their Borel right...