Atmospheric dynamics Introduction 1 Equations of Motion 2 Thermodynamics and Energetics 3 Elementary Properties and Applications 4 Vortex Dynamics 5 The Dynamics of the Shallow Water Equations 6 The Stratified Atmosphere 7 The Planetary Boundary Layer 8 Wave Mean Flow Interaction 9 The Meridional Circulation 10 Gravity Waves 11 Appendix A Useful Elements of Vector Analysis Appendix B Rotations Appendix C Isotropic Tensors Appendix D Spherical Coordinates Appendix E Fourier Integrals and Fourier Series Appendix F Zonally Symmetric Rossby Waves Appendix G Solution of an Initial Value Problem Appendix H Some Polarization Relations Appendix I The Higher Harmonics of a Gravity Wave Field in WKB Theory. This textbook is intended for both undergraduate and graduate courses in meteorology and atmospheric sciences as well as for researchers working on theoretical and numerical aspects of weather and climate or on geophysical fluid dynamics. The treatment is concise thorough and self contained. All necessary concepts are introduced and the reader is given explicit guidance on all mathematical steps. The book begins with a derivation of the equations of motion. These are then used to discuss fundamental aspects of weather and climate. The mechanisms behind vortical motions that are known from the daily weather map are discussed. Shallow water theory is introduced as a tool for an efficient analysis of key concepts such as atmospheric waves and synoptic scale vortices. Quasigeostrophic theory is described and then used to explain the occurrence and mechanisms of extratropical weather by means of baroclinic instability. The specific properties of the atmospheric boundary layer are discussed with a focus on the interaction between turbulence and mean flows. This is followed by a detailed look at the global atmospheric circulation highlighting its control by Rossby waves and gravity waves. At the same time the reader is introduced to essential concepts that find applications in the field such as balance by geostrophic and hydrostatic equilibrium the role of entropy and potential temperature potential vorticity the Kelvin theorem instability theory the Reynolds equations Eliassen Palm and pseudo momentum flux multi scale asymptotics WKB theory wave action the transformed Eulerian mean critical layers and wave refraction. The text is supplemented by appendices on important mathematical concepts and further elaborations of the main text. Chapter summaries and reading recommendations help the reader not merely to keep focus on the essentials but just as well to broaden the horizon. The Author Ulrich Achatz holds the chair for the Theory of Atmospheric Dynamics and Climate at Goethe Universität Frankfurt. He has a diploma in physics and a PhD in astronomy both from the University of Bonn and a habilitation degree in atmospheric physics from the University of Rostock. His research interests focus on the interaction of atmospheric motions with different scales from turbulence over gravity and Rossby waves to the global atmospheric circulation and its reliable description in weather and climate codes.