This analysis seeks to present macroscopic irreversible thermodynamics in its realm and its splendour by appealing to the notion of internal variables of state. This applies to both fluids and solids with or without microstructures of mechanical or electromagnetic origin. This unmatched richness of essentially nonlinear behaviours is the result of the use of modern mathematical techniques such as convex analysis in a clear-cut framework which allows one to put under the umbrella of irreversible thermodynamics behaviours which until now have been commonly considered either not easily covered, or even impossible to incorporate into such a framework. The book is intended for all students and researchers whose main concern is the rational modelling of complex and/or new materials with physical and engineering applications, such as those accounting for coupled-field, hysteresis, nonlinear-diffusion, and phase-transformation phenomena.