This book presents for the first time in the German language how the mathematical formalism and phenomena of quantum mechanics arise from a fundamental mechanical theory, namely Bohmian mechanics. This is analogous to the idea of explaining macroscopic phenomena from microscopic fundamental laws. This program is carried out here with complete mathematical rigor, introducing and explaining the necessary methods and foundational insights. After a detailed presentation of the fundamentals, the author addresses the statistical analysis of Bohmian mechanics and develops the fundamental concepts of quantum mechanics from this, including scattering theory, which has not been presented in this form before. The book sheds new light on the foundational problems and paradoxes of quantum mechanics and connects them rigorously.