This is the first comprehensive monograph on a new thermodynamic theory that goes beyond the classical theory of irreversible processes. In contrast to the classical approach, the local equilibrium hypothesis is abandoned, and the basic variables are complemented by non-equilibrium quantities. The claims made for 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 present edition reflects new developments in the theory of applications, adds new problems and provides a more detailed comparison with other fields of active research.