This textbook covers classical statistical mechanics and quantum statistics, going well beyond standard material in the topics discussed. For example, it addresses the theory of white dwarfs and the role of strict infrared bounds for the existence of phase transitions. In the first part, the author develops the fundamentals of classical statistical mechanics, followed by many applications that illustrate the scope of the theory well. A focus is placed on the investigation of phase transitions. The role of the renormalization group in second-order phase transitions is presented in detail. In the third part, the foundations of quantum statistics are developed. In addition to standard applications, further advanced topics are also covered, such as the proof of the Mermin-Wagner theorem for Heisenberg models. This textbook is comprehensive.