The equations of thermoelasticity describe the elastic and the thermal be havior of elastic, heat conductive media, in particular the reciprocal actions between elastic stresses and temperature differences. We consider the classi cal thermoelastic system where the elastic part is the usual second-order one in the space variable. The equations are a coupling of the equations of elas ticity and of the heat equation and thus build a hyperbolic-parabolic sys tem. Indeed, both hyperbolic and parabolic effects are encountered. This book discusses the mathematical questions arising in the study of initial value problems and of initial boundary value problems to these equations, both for linear and for nonlinear systems. Classical boundary conditions of the Dirichlet type — rigidly clamped, constant temperature — or the Neumann type — traction free, insulated — are considered, as well as the linearized equations together with contact boundary conditions.