Anyone who has always wanted to understand the hieroglyphs on Sheldon's blackboard in the television series The Big Bang Theory or who wanted to know exactly what the fate of Schrodinger's cat is all about will find a short, descriptive introduction to the world of quantum mechanics in this essential. In particular, the text focuses on the mathematical description in the Hilbert space. The content goes beyond popular scientific presentations, but is nevertheless suitable for readers without special prior knowledge thanks to the clear examples. This Springer essential translation of the original German was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors. The author has been Professor of Mathematics and Simulation at the FH Aachen since 2011. Before he was appointed to the FH Aachen, he was a research assistant in the Optimization department of the Fraunhofer Institute for Industrial Mathematics.