Physics, Mathematics, and Engineering have been complimenting each other for the past two centuries; and mutual interaction between them has enriched the mankind in many ways. This book deals with the concept of thermo elasticity which finds its roots and application in the above branches. Mathematical aspects of thermo elastic problems in different geometric structures have been dealt with. Thermal displacements, Thermal stress and strains in these structures have been discussed in detail. Morever, FGM, which are fast emerging as high thermal stress bearing materials have been discussed. Magneto-thermoelastic stresses and magnetic field vector perturbations for FGM hollow cylinder, Orthotropic solid cylinder, FGM hollow sphere have been deduced. Mathematical approach for thermoelastic problems may be of immense use for the researchers, teachers pursuing work on thermoelasticity.