The basic themes in all parts of this book are point process theory, the Poisson and compound Poisson processes. Point processes constitute an important part of modern stochastic process theory. They are well understood models and have applications in a wide range of applied probability areas such as stochastic 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 major 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. Parts I and II of this text are kept at a level which requires basic knowledge of probability theory and stochastic processes. Such knowledge is typically available in the 2nd or 3rd year of a bachelor program with a mathematical, statistical, actuarial or econometric orientation.