This book is a comprehensive study of the life and mathematics of Walter Noll, the creator of the mathematical tools of modern rational mechanics and thermodynamics. The book stresses particularly Noll’s method of axiomatization of physical theories, his axiomatics of continuum mechanics, thermodynamics of materials, special relativity theory, his discovery of the neo-classical space-time of mechanisms, his theories of inhomogeneities in simple bodies, fit regions, contact interactions, and annihilators of fluid mechanics.