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This monograph offers a fundamentally new approach to facilitate the study of metabolic networks in cells. It aims to overcome the limitations of either just a single FBA solution, or an overwhelming number of extreme pathways in a realistic network. Instead it focusses on the FBA solution space and describes it in a simplified way by extracting just a bounded subspace: the Solution Space Kernel or SSK. This reduces the relevant number of flux space dimensions by orders of magnitude, and allows its location, size and shape to be characterised. It is a multi-stage process, requiring many new concepts and algorithms for manipulating polytopes in high dimensional spaces.The book introduces and develops these concepts in a pragmatic way that takes into account the difficulties of performing analyses in a flux space with dimensions counting in the hundreds or thousands. It emphasizes the details of implementation in computational code and applications to realistic models are demonstrated. For many cases, the number of constraints and flux variables that fully specify the SSK polytope is only a single or double-digit number. This allows the range of metabolic states accessible to a cell to be further interpreted geometrically in terms of a manageable set of orthogonal diameters and aspect ratios. In addition, explicit representative fluxes, giving the centre and periphery of the solution space kernel, become available for further exploration.