Liquid 4He and 3He are the purest Bose and Fermi liquids currently found in nature. Understanding their dynamics is fundamental to understanding more complex matter. This book provides an introduction to the subject and develops the theory of zero sound, phonons, rotons, spin and single particle excitations in quantum solids and fluids. Similarities between quantum solids and fluids are drawn wherever possible. Topics include dynamic response functions, neutron studies of solid helium, the nature of excitations in 3He, approximations to the dynamic susceptibility, and intermediate and high momentum transfer, among many others. In offering a critical comparison between theory and up-to-the-minute experimental data, the book provides a comprehensive assessment of our current understanding of collective and single particle excitations in quantum liquids and solids.