An exciting monograph of some new applications of so-called pure mathematics, including number theory, to various problems arising in quantum field theory. A self-contained unique treatment using conventional math terminology. Introductory material on Planck, Schr"dinger quantization, Paulis spin functions, multielectron atoms; more advanced topics include: Feynman path integrals, quantum partition functions, zeta functions, spherical harmonic analysis and the Selberg trace formula. Good bibliography and index. An excellent resource for clasroom or self-study.