This book offers a historical analysis of Bartel Leendert van der Waerden's early contributions to quantum mechanics; in particular, focusing on his role in the development and application of group-theoretic methods around 1930. While van der Waerden is widely known for his modern algebra, his engagement with quantum theory has received little attention in the historical literature. Through careful study of published and archival sources, the author reconstructs the contexts in which van der Waerden worked, and examines his networks as well as his interactions with contemporaries such as Hermann Weyl, Eugene Wigner, Paul Ehrenfest, and John Slater. By comparing the different emerging approaches of adapting group-theoretic methods to problems in quantum mechanics, the author shows that van der Waerden stands out as a rather pragmatic and undogmatic thinker. Special attention is given to reconstructing a more nuanced picture of the arising controversy around the ""group plague"" in quantum mechanics. Combining technical exposition with biographical and historical analysis, the book is intended for mathematicians, physicists, and historians of science. The reader is expected to have beginning, graduate-level knowledge of mathematics-mainly algebra and, in particular, representation theory-as well as some background in quantum physics. The study sheds light on a complex and fascinating period in the development of mathematical physics. It explores the dynamics of the interactions between mathematics and physics, and thus contributes to ongoing discussions about mathematization processes in science in the twentieth century.