This expanded document offers a gentle yet scientific introduction to the hot topic of full waveform inversion (FWI) with a focus on its practical application to anisotropic media. The book includes discussion of a mix of classical developments in FWI based on a simple framework, as well as critical new developments that address current challenges. Recent FWI case study results, as well as our experience with imaging seismic data, suggest the necessity of taking the anisotropic nature of the Earth into consideration. Unlike elasticity or attenuation, anisotropy actually effects the kinematics of the wavefield, in addition to the amplitudes. Many practical implementations of FWI ignore the elastic nature of the Earth and use the S-wave free, acoustic assumption by reducing the impact of amplitudes. The importance of including at least acoustic amplitudes is, however, becoming more and more apparent. The goal of this book is to provide a recipe for practical anisotropic FWI, with proper FWI setups and anisotropy parameter representations. - from Amzon