In this dissertation we have presented 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 optimisation strategies. An extensive treatment of the kinematics of filament winding is here presented, in combination with several recommendations for a proper derivation of the associated velocities and accelerations to which the moving machine parts and the roving itself are subjected. A simplified collision control module has resulted in the determination of the limits where the feed eye is allowed to move in. Within this space and with the dynamic machine limits, an optimisation problem has been set up, serving the aim of production time minimisation. This has been achieved by application of dynamic programming that minimises a summation of constraint respecting time increments, after the realisation of a grid-reduction with a technique that is based on elementary sparse matrix multiplication. Furthermore, several novel machine configurations have been proposed, which are dedicated to pressure vessels with various aspect ratios, shape morphology and types of applied wound circuits. With the shell equilibrium equations as a basis, we have derived the class of articulated pressurisable structures, comprising isotensoids that are axially stacked on each other. Moreover, the non-geodesically overwound isotensoid has been introduced, together with a variant being additionally subjected to external radial forces. The same equilibrium equations have generated shapes like the geodesically overwound hyperboloid and optimal toroidal pressure vessels. Furthermore, we have proposed several application fields for these items. As a leitmotiv throughout the thesis, the derived methodologies and equations have been applied on the class of isotensoid pressure vessels. The results generated by the roving trajectories description modules and pattern generation algorithms are verified by simulation, while the results of the kinematic solver and the optimiser are evaluated by both simulation and implementation on a winding machine. However, mechanical testing of the proposed structures and test-running of the introduced machine configurations must here be left over to the recommendations.