This is the first volume of a three-volume introduction to modern geometry, with emphasis on applications to other areas of mathematics and theoretical physics. Topics covered include tensors and their differential calculus, the calculus of variations in one and several dimensions, and geometric field theory. This material is explained in as simple and concrete a language as possible, in a terminology acceptable to physicists. The text for the second edition has been substantially revised.

Introduction In the present essay, we attempt to convey some idea of the skeleton of topology, and of various topological concepts. It must be said at once that, apart from the necessary minimum, the subject-matter of this survey does not indude that subdiscipline known as "general topology" - the theory of general spaces and maps considered in the context of set theory and general category theory. (Doubtless this subject will be surveyed in detail by others. ) With this qualification, it may be daimed that the "topology" dealt with in the present survey is that mathematieal subject whieh in...

Introduction In the present essay, we attempt to convey some idea of the skeleton of topology, and of various topological concepts. It must be said at once that, apart from the necessary minimum, the subject-matter of this survey does not indude that subdiscipline known as "general topology" - the theory of general spaces and maps considered in the context of set theory and general category theory. (Doubtless this subject will be surveyed in detail by others. ) With this qualification, it may be daimed that the "topology" dealt with in the present survey is that mathematieal subject whieh in...