Over the last few years, anisotropy has become a "hot topic" in seismic exploration and seismology. It is now recognised that geological media deviate more or less from isotropy. This has consequences for acquisition, processing and interpretation of seismic data and also helps determine the cause of anisotropy and adds to our knowledge concerning the structure of the medium at scales beyond the resolution of the seismic method. This volume addresses the theoretical foundations of wave propagation in anisotropic media at an easily accessible level. The treatment is not restricted to exploration seismology. The book commences with fundamental material and covers the description of wave propagation in anisotropic conditions by means of slowness and wave surfaces. It continues to explore the theory of elasticity, the interaction of elasticity and material symmetry and conditions imposed by the stability of the medium. Wave propagation in general anisotropic solids are discussed referring in particular to singular and longitudinal directions. Slowness and wave surfaces in transversely isotropic media and in the planes of symmetry of orthorhombic media is presented and then moves on to wave propagation in orthorhombic media by means of "squared slowness surfaces". The latter part of the book deals with layer-induced anisotropy showing how a particular internal structure of a medium leads to anisotropy and how much of this structure can be recovered by "inversion" of the modelling algorithm. A few fundamental aspects of exploration seismology are also discussed. The final chapter discusses how concepts which were developed by Kelvin, but only recently understood, can be utilised to determine the symmetry class and orientation of an elastic medium.