This is the first comprehensive monograph on a new thermodynamic theory that goes beyond the classical theory. In contrast to the classical approach, the local equilibrium hypothesis is abandoned, and the basic variables are complemented by non-equilibrium quantities. The statements behind extended thermodynamics are confirmed by the kinetic theory of gases and statistical mechanics. The book covers a wide spectrum of applications, and also contains a wide discussion of the foundations and the scope of the most current theories of non-equilibrium thermodynamics. The new edition reflects new developments and contains a new chapter on the interplay between hydrodynamics and thermodynamics, a field of active research.