"Seismological Attenuation without Q" represents a comprehensive and critical review of the present approach to describing the seismic-wave attenuation within the Earth. Starting from first physical principles, author Igor B. Morozov shows that the existing model of attenuation based on the concept of quality factor, or Q, is inadequate and represents only a phenomenological model. In most cases, Q should not be interpreted as a physical property of the Earth's medium. This text offers an alternate view developed using the concept of attenuation coefficient and illustrated using many theoretical and data examples. The new approach leads to significant advances in understanding the physics of Earth's anelasticity, measurement, and modeling attenuation of seismic waves. A systematic and hitherto unseen pattern of attenuation coefficients is recognized within a broad range of wave types and frequencies, which leads us to a general and clear picture of the attenuation structure of the Earth. At the same time, Morozov also elucidates a number of unsolved problems, such as numerical modeling and inversion for seismic attenuation and understanding its relation to the structure and the physical state of the deep Earth. Most notably, "Seismological Attenuation without Q" shows that the attenuation problem is significantly more complex than presented in the Q-based, visco-elastic model.