This textbook is written for graduate students and researchers in meteorology and related sciences. 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. The authors start by introducing the equations that describe the basic laws of thermodynamics and entropy and go on to discuss the thermodynamics of blackbody radiation, thermodynamic potentials, and the constitutive equations of irreversible fluxes. Later chapters look at the state functions of ideal gases, thermodynamics of cloud air, heat equations for special adiabatic systems, atmospheric statics, stability, and 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 exercises are given at the end of the book.