Mechanical spectroscopy is a non-destructive technique that is very well suited for studying the dynamics of singularities such as structural defects in solids. It has been successfully applied in solid state physics and materials science for more than fifty years, and the present textbook aims at summarising the state-of-the-art in this field by presenting recent results obtained in Western European laboratories. The contents are divided into nine chapters. Introduction to mechanical spectroscopy (Ch.1) is based on a complete description of the elastic, viscoelastic, and viscoplastic behaviours of solids. The anelastic response is analysed from three different viewpoints: phenomenology, rheology and thermodynamics.