Liquid 4He and 3He are the purest Brose and Fermi liquids currently available in nature. Understanding the dynamics and excitations of those quantum systems is a fundamental issue of science and a guide for more complex matter. The book develops the theory of zero sound, phonons, rotons, spin and single particle excitations in quantum solids and fluids in an historical context. The book brings the theory up to date in modern language with similarities between quantum solids and fluids drawn wherever possible. A survey of recent neutron scattering data in each system is presented. A critical comparison of theory and recent data provides a comprehensive assessment of our current understanding of collective and single particle excitations in quantum liquids and solids.