"The Mathematical Aspects of Quantum Maps" offers a comprehensive examination of the mathematical foundations of quantum maps, which play a crucial role in understanding quantized chaotic systems. The book places particular emphasis on the physical origins of these concepts and serves as a testing ground for the application of modern mathematical methods from analytical and algebraic number theory. It addresses both the theoretical and numerical aspects of quantum chaos research, including the calculation of eigenvalues and eigenfunctions for chaotic quantum systems. The content is designed for both scientists and advanced students in the fields of mathematics and mathematical physics, providing deep insights into the mathematical challenges that arise in this exciting area of research.