The second edition of this book contains both basic and more advanced - terial on non-life insurance mathematics. Parts I and II of the book cover the basic course of the 1rst edition; this text has changed very little. It aims at the undergraduate (bachelor) actuarial student as a 1rst introduction to the topics of non-life insurance mathematics. Parts III and IV are new. They can serve as an independent course on shastic models of non-life insurance mathematics at the graduate (master) level. The basic themes in all parts of this book are point process theory, the Poisson and compound Poisson processes. Point processes constitute an - portant part of modern shastic process theory. They are well understood models and have applications in a wide range of applied probability areas such as shastic geometry, extreme value theory, queuing and large computer networks, insurance and finance. The main idea behind a point process is counting. Counting is bread and butter in non-life insurance: the modeling of claim numbers is one of the - jor tasks of the actuary. Part I of this book extensively deals with counting processes on the real line, such as the Poisson, renewal and mixed Poisson processes. These processes can be studied in the point process framework as well, but such an approach requires more advanced theoretical tools.