This book is an introductory text on seismology intended for upper division undergraduates and graduate students. The book emphasises fundamental concepts and basic mathematical developments, and is intended to be 'student friendly'. The author explains the fundamental concepts in full detail with step-by-step development of the mathematics, although the book does assume a knowledge of vector and tensor analysis, calculus and ordinary and partial differential equations, as well as of fundamental physics, especially mechanics and elasticity theory. Simple examples, such as one-dimensional problems and liquid media are used as introductory topics. The book covers most of the fundamental topics in seismology, including seismic wave propagation, normal mode theory, ray theory approximation, body and surface waves, source mechanisms, kinematic and dynamic models and applications to the understanding of the structure of the Earth and seismotectonics. The book also contains appendices on useful mathematical tools and includes extensive problems.