Historical Introduction -- The Standard Model of Elementary Particles -- Kinematics and Cross Sections -- Physics of Particle and Radiation Detection -- Acceleration Mechanisms -- Primary Cosmic Rays -- Secondary Cosmic Rays -- Cosmology -- The Early Universe -- Big Bang Nucleosynthesis -- The Cosmic Microwave Background -- Inflation -- Dark Matter -- Astrobiology -- Outlook -- Solutions.The book describes the branch of astrophysics in which processes in the universe are investigated with experimental methods known from particle physics experiments. After a historical introduction to the basics of elementary particles, their interactions and the relevant detection techniques are described. The main body of the book concerns cosmic rays. The modern aspects of astroparticle physics are described in a chapter on cosmology. The book provides an orientation in the field of astroparticle physics that many beginners might look for. The physics issues are presented with little mathematics, and the results are illustrated by many diagrams. The reader has a chance to enter this field of astrophysics with a book that closes the gap between expert and popular level.