In mathematics and the sciences, just as in the arts, there is no substitute for the masterpieces. Fortunately, both in Differential Geometry and in Continuum Mechanics, we possess a veritable treasure trove of fundamental masterpieces, classical as well as modern. Reading them may elicit a pleasure, even an emotion, comparable to that aroused by playing a Mozart piano sonata, the same sensation of perfection and beauty, the sweetness of drowning in such an ocean. This comparison is fair also in a different sense, namely, that for common mortals to achieve these spiritual heights requires a considerable amount of study and work, without which we must resign ourselves to the intuitive feelings evoked by the senses and to the assurances of the critics or the arbiters of taste. The aim of this book is to provide some familiarity with the basic ideas of Differential Geometry as they become actualized in the context of Continuum Mechanics so that the reader can feel more at home with the masters.

Differential Geometry is a rather sophisticated blend of Algebra, Topology, and Analysis. My selection of topics as a nonmathematician is rather haphazard and the depth and rigor of the treatment vary from topic to topic. As befits human nature, I am understandably forgiving of myself for this lack of consistency, but the reader may not be so kind, in which case I will not take it as a personal offence.