The vibrations of atoms inside crystals - lattice dynamics - is basic to many fields of study in the solid-state and mineral sciences. Lattice dynamics is becoming increasingly important for work on mineral stability. This book provides a self-contained text that introduces the subject from a basic level and then takes the reader through real applications of the theory. The book is aimed at advanced undergraduates, graduate students and research workers in the earth and solid-state sciences who need to incorporate lattice dynamic treatments into their work. Applications include the use of lattice dynamics instabilities to study the origin of phase transitions in crystals and the use of vibrational spectra to obtain information about inter-atomic forces.