This volume focuseson the relevant general theory and presents some first applications, namelythose based on classical shell theory. After a brief introduction, during whichthe history and state-of-the-art are discussed, the first chapterpresents the mechanics of anisotropic heterogeneous shells, covering allrelevant assumptions and the basic relations of 3D elasticity, classical andrefined shell models. The second chapter examines the numerical techniques thatare used, namely discrete orthogonalization, spline-collocation and Fourierseries, while the third highlights applications based on classical theory, inparticular, the stress-strain state of shallow shells, non-circular shells,shells of revolution, and free vibrations of conical shells. The book concludeswith a summary and an outlook bridging the gap to thesecond volume.