This is Ph.D. dissertation presents an overview and comprehensive treatment of several facets of the filament winding process. With the concepts of differential geometry and the theory of thin anisotropic shells of revolution, a parametric shape generator has been formulated for the design procedure of optimal composite pressure vessels in particular. The mathematical description of both geodesic and non-geodesic roving trajectories has been presented, including a proposal for a mandrel shape that facilitates the experimental procedure for the determination of the coefficient of friction. In addition, an overview of several (non-) geodesic trajectories is here given. Furthermore, an algorithm for the automatic generation of suitable winding patterns has been outlined, in combination with several pattern optimization strategies.Koussios, Sotiris is the author of 'Filament Winding A Unified Approach', published 2004 under ISBN 9789040725517 and ISBN 9040725519.