Introduction -- Model Hierarchy and Simplified Climate Models -- Describing Transports of Energy and Matter -- Energy Transport in the Climate System and its Parameterisation -- Initial Value and Boundary Value Problems -- Large-scale Circulation in the Ocean -- Large-scale Circulation in the Atmosphere -- Atmosphere-Ocean Interactions -- Multiple Equilibria in the Climate System -- Index. A three-tier approach is presented: (i) fundamental dynamical concepts of climate processes, (ii) their mathematical formulation based on balance equations, and (iii) the necessary numerical techniques to solve these equations. This book showcases the global energy balance of the climate system and feedback processes that determine the climate sensitivity, initial-boundary value problems, energy transport in the climate system, large-scale ocean circulation and abrupt climate change.