Thermodynamics of irreversible processes can be included into the framework of Lagrange formalism. This formalism presents a unifred method for reversible and irreversible processes. As a remarkable fact the first and the second law of thermodynamics are derived in La,orange formalism by means of straightforward procedures. The whole information on the dynamics of a system is included in one function only, namely in its Lagrangian. In this paper the theory is presented in two courses. The first one offers an almost qualitative insight into the structure of the theory; the second one is concerned with the associated mathematics in some detail. The theory is illustrated by three representative examples: the style of the paper is chosen as to stimulate the discussions at a workshop and a school on the state-of-art of non-equilibrium thermodynamics of complex fluids, Oxford, 2000.