It is a feature of the history of the subject that the study of atomic physics was accompanied by a partial neglect of that of classical mechanics. This led to the unsatisfactory situation in which the physicist was expected to assimilate the elements of quantum and statistical mechanics without understanding the classical foundations on which these subjects were built. The situation has improved in recent years through the general lengthening of degree courses, and it is now usual to study the analytical formulation at the late under- graduate stage. A number of excellent treatises are available, and there are also many elementary accounts to be found in general works on physical principles. However, there has been available so far no self-contained introduction to the subject which provides the beginner with a broad general review without involving him in too much detail. It is hoped that this book may bridge the gap by pro- viding the experimental physicist with a sufficient background for his theoretical understanding and the theorist with some stimulus to study the masterpieces of the subject. The mathematical equipment required is no more than in the normal honours physics course. For the purposes of Chapters IX- XI it includes an elementary knowledge of cartesian tensors. A familiarity with Newtonian mechanics and some acquaintance with special relativity theory are presumed, though summarizing accounts are also given.