Writing this book, I had in my mind areader trying to get some
knowledge of a part of the modern differential geometry. I
concentrate myself on the study of sur faces in the Euclidean
3-space, this being the most natural object for investigation. The
global differential geometry of surfaces in E3 is based on two
classical results: (i) the ovaloids (i.e., closed surfaces with
positive Gauss curvature) with constant Gauss or mean curvature are
the spheres, (u) two isometrie ovaloids are congruent. The results
presented here show vast generalizations of these facts. Up to now,
there is only one book covering this area of research: the Lecture
Notes [3] written in the tensor slang. In my book, I am using the
machinary of E. Cartan's calculus. It should be equivalent to the
tensor calculus; nevertheless, using it I get better results (but,
honestly, sometimes it is too complicated). It may be said that
almost all results are new and belong to myself (the exceptions
being the introductory three chapters, the few classical results
and results of my post graduate student Mr. M. AEFWAT who proved
Theorems V.3.1, V.3.3 and VIII.2.1-6).
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