This textbook is written for graduate students and researchers in meteorology and related sciences. To encourage the reader to follow in detail the mathematical developments, the derivations are complete leaving out only the most elementary steps. While most meteorological textbooks only present equilibrium thermodynamics, this book also introduces the linear theory of non-equilibrium and provides the necessary background for more advanced studies. It is designed to complement the authors' previous text, Dynamics of the Atmosphere (Cambridge, 2003). The bookstarts with an introduction to the basic concepts, including the general form of the budget equation. The authors show how to derive the prognostic equations for temperature that follow from the development of the first law of thermodynamics. They then go on to discuss the second law of thermodynamics. The entropy production equation is introduced on the basic of Gibbs' fundamental equation and the calculation of entropy changes is demonstrated. A brief treatment of the thermodynamics of blackbody radiation is followed by a detailed discussion of thermodynamic potentials. Of great importance are the constitutive equations of irreversible fluxes, which are described in connection with the Onsager-Casimir reciprocity relations. Later chapters discuss the state functions of ideal gases, of the condensed pure phase, and the state functions, as well as the thermodynamics of cloud air. The heat equations for special adiabatic systems are described and the authors introduce the use of graphical procedures to evaluate atmospheric variables. The final chapter presents essential topics of atmospheric statics making use of such concepts as homotropy, barotropy, heterotropy, and piezotropy. This chapter contains a thorough discussion of stability and of atmospheric energetics of hydrostatic equilibrium. Each chapter ends with a set of exercises that are designed to help the reader develop a deeper understanding of the subject. Answers to all the exercices are given at the end of the book.