The present volume deals with the derivation of the basic system of equations and boundary conditions, surface waves, inertial and planetary waves, and with ocean currents. Two-layered ocean models are included. We refer to them as quasi homogeneous models; the solutions obtained are basically the same as for a homogeneous ocean. The knowledge of mathematics assumed is that of introductory courses in advanced calculus and differential equations. Some basic relations from vector analysis are reviewed in the first three sections of chapter 1. Chapter 1 of this volume is devoted to basic hydrodynamics. The boundary conditions are of major importance for oceanography, because so many of the forces to which the ocean responds, act at the sea surface. To give a unified theory of the field equations and the boundary conditions, which replace the field equations at an interface, they are all derived from the same general conservation law. Chapter 2 deals with periodic processes, perturbation theory and linear systems, which are needed for the subsequent chapters. The theory of gravity and capillary waves is treated in chapter 3. The theory of the development of wind-generated ocean waves has been excluded, because this seems to be one of the major stochastic processes in the ocean. It is, therefore, beyond the scope of this volume. Chapter 4 is devoted to inertial and planetary waves, chapter 5 deals with the theory of ocean currents.
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