This book is an original and timeless description of the elasticity of solids, and more particularly of crystals, covering all aspects from theory and elastic constants to experimental moduli. The first part is dedicated to a phenomenological and dimensionless representation of macroscopic crystal elasticity, which allows us to compare all crystals of the same symmetry with the concept of anisotropy and to establish new relations between elastic constants. Multi-scale approaches are then put forward to describe the elasticity at an atomic scale or for polycrystals. The relationship between elasticity and structural or physical properties is illustrated by many experimental data. The second part is entirely devoted to a Lagrangian theory of vibrations and its application to the characterization of elasticity by means of the dynamic resonant method. This unique approach applied to tension-compression, flexural and torsional tests allows for an accurate determination of elastic moduli of structural and functional crystals, varying from bulk to multi-coated materials.