This graduate and research-level book applies the methodology of dynamical systems theory to investigate the physics of the global ocean circulation, e.g. the dynamics of the Gulf Stream separation and the El Niño/Southern Oscillation phenomenon. It also deals with the numerical methods for applying bifurcation analysis to large dimensional dynamical systems, which arise through discretization of ocean models. Systematic analysis within a hierarchy of models using these techniques leads to a novel approach in understanding the phenomena of climate variability, and an overview is obtained of the relations between the results of the different models within the hierarchy. Mechanistic description of the physics of the results is provided and, where possible, links with results of state-of-the-art models and observations are sought. Each chapter is essentially self-contained and many details of derivations are provided. The second edition has been updated throughout. Exercises presented at the end of each chapter make it a perfect graduate-level text.