This new book examines the numerous thermodynamic inequalities and their applications to transport problems, in gases and magnetoplasmas. The author develops the theory of irreversible thermodynamics in the text, both for continuum and kinetic theory descriptions. To provide an overview of the principal ideas, a historical introduction is given at the start of the book. The book spans a wide range of thermodynamics historical, classical, irreversible, continuum, kinetic - for gases and magnetoplasms. This work gives coverage to large amounts of vital material found in no other text.