This textbook introduces the reader to quantum theory and quantum chemistry. The textbook is meant for 2nd - 3rd year bachelor students of chemistry or physics, but also for students of related disciplines like materials science, pharmacy, and bioinformatics. At first, quantum theory is introduced, starting with experimental results that made it inevitable to go beyond classical physics. Subsequently, the Schroedinger equation is discussed in some detail. Some few examples for which the Schroedinger equation can be solved exactly are treated with special emphasis on relating the results to real systems and interpreting the mathematical results in terms of experimental observations. Ultimately, approximate methods are presented that are used when applying quantum theory in the field of quantum chemistry for the study of real systems like atoms, molecules, and crystals. Both the foundations for the different methods and a broader range of examples of their applications are presented. The textbook assumes no prior knowledge in quantum theory. Moreover, special emphasis is put on interpreting the mathematical results and less on an exact mathematical derivations of those. Finally, each chapter closes with a number of questions and exercises that help in focusing on the main results of the chapter. Many of the exercises include answers.