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This first volume in the treatise on the Physics of Lakes deals with the formulation of the mathematical and physical background. A large number of lakes on Earth are described, presenting their morphology as well as the causes of their response to the driving environment. Because the physics of lakes cannot be described without the language used in mathematics, these subjects are introduced first by using the most simple approach and with utmost care, assuming only a limited college knowledge calculus and classical Newtonian physics, and continue with increasing complexity and elegance. Starting with the fundamental equations of Lake Hydrodynamics in the form of "primitive equations" and leading to a detailed treatment of angular momentum and vorticity.