This textbook is a concise but comprehensive introduction to the central theoretical concepts of modern astrophysics. It aims at students at graduate level and lecturers that teach courses in theoretical astrophysics or advanced topics in modern astronomy. This book with its abundant examples and exercises serves also as reference and entry point for more advanced researchers who want to update their knowledge of the physical processes that govern behavior and evolution of astronomical objects. The author illustrates a small number of fundamental physical methods and principles which are sufficient to describe and understand a wide range of at first glance very diverse astrophysical phenomena and processes. For example, the formulae that lay out the macroscopic behavior of gases and fluids, of stellar systems, as well as of the radiation field, all are derived in the same way from the microscopic distribution function using a local averaging procedure together with taking central moments of the distribution. The microscopic distribution function itself can be obtained from fundamental kinetic theory. A discussion of these relations constitutes the second chapter of this book. The concept of distribution functions and derive Boltzmann's equation is defined. Furthermore, the equilibrium distribution function for ideal gases is calculated, and small perturbations and their relaxation back to the equilibrium state are discussed. Finally, the author describes that macroscopic quantities are usually associated with moments of the distribution function and derive their evolutionary equations.