Recent advances in our understanding of instabilities in galactic type systems have led to an unravelling of some of the mysteries of what determines the form galaxies take. This book focuses on the mathematical development of the subject, assuming no prior knowledge of it, with a strong emphasis on the underlying physical interpretation. This framework is used to discuss the most relevant instabilities which are believed to be closely involved in the way galaxies are formed, in a model independent manner. The relevant observed properties of galaxies that may be used to establish the role of these physical mechanisms are discussed. The book also includes a chapter discussing numerical simulation techniques, with attention paid to their limitations and to recent advances in this approach. It is demonstrated that recent developments in computer hardware enable a detailed comparison of simulations with analysis. Thus the simulations extend our physical understanding beyond the limitations of the analysis. The book is intended for use by postgraduate students and researchers in the areas of cosmology, extragalactic astronomy and dynamics.