The aim of this book is to present up-to-date methodologies in the analysis and optimization of the elastic stability of lightweight statically determinate, and in- determinate, space structures made of flexible members which are highly stiff when loaded centrally at the nodes. These are flat and curved space pin- connected open or enveloped lattices and reticulated shells which, due to their high loadbearing capacity to weight ratios, are gaining in importance in aerospace and other fields. They are utilized, for example, in space stations, as support structures for large radio-telescopes and for other equipment on earth and in outer space, as roof structures for the coverage and enclosure of large areas on earth and as underwater shell-type structures enveloped by a cover-shell capable of withstanding high hydrostatic pressures. • Space structures of this type are generally subjected to considerable internal axial loads in the flexible members and they fail through the loss of global statical stability, usually precipitated by the intrinsic small imperfections at finite near-critical elastic deformations - and not primarily by the the break-down of the material of which they are made, as is the case in conventional systems. Thus, the criterion in the design of such structures calls for eliminating or isolating the onset of the elastic dynamic collapse thereby increasing their safe stability limit. • Standard finite element methods, as they are employed by most users today, are totally inadequate for such analyses since they do not account for the choice of the branching paths in the loading process of the structure nor for the existence of the relevant collapse modes. • These aspects are novel and they are presented here for the first time in comprehensive book form.