This textbook provides a mathematical introduction to the theory of large-scale ocean circulation and is accessible for readers with an elementary knowledge of mathematics and physics, including continuum mechanics and solution methods for ordinary differential equations. The book consists of four parts. Part I (chapters 1 - 4) is a very brief introduction to ocean circulation and the mathematical formulation of the governing equations of ocean flows. In addition, concepts are introduced that are necessary to describe and understand large-scale ocean currents. In part II (chapters 5 - 10), the theory of mid-latitude wind-driven ocean circulation is presented. The consideration of model development includes a top-down approach and reduced equations are derived using asymptotics and scaling. Part III (chapters 11 - 12) focuses on the understanding of equatorial currents and El Nino. In the last part IV, chapters 13 - 16, the theory of planetary scale flows is presented, covering topics such as the thermocline problem, the Antarctic Circumpolar Current, the stability of the thermohaline circulation and the Arctic Ocean circulation. At the end of each chapter several exercises are formulated. Many of these are aimed to further develop methodological skills and to get familiar with the physical concepts. New material is introduced in only a few of these exercises. Fully worked out answers to all exercises can be downloaded from the book web site.
