This book focuses on the need for an Eulerian formulation of constitutive equations. After introducing tensor analysis using both index and direct notation, nonlinear kinematics of continua is presented. The balance laws of the purely mechanical theory are discussed along with restrictions on constitutive equations due to superposed rigid body motion. The balance laws of the thermomechanical theory are discussed and specific constitutive equations are presented for: hyperelastic materials; elastic-inelastic materials; thermoelastic-inelastic materials with application to shock waves; thermoelastic-inelastic porous materials; and thermoelastic-inelastic growing biological tissues.