High-energy catalytic processes operated in fixed bed reactors are widely used in many fields of chemical engineering, so the improvement of specific intensities of such processes to minimise the equipment size and related capital cost, to enhance the reliability is of great importance. The specific features of such processes are reactant concentration gradients through the bed length which may cause considerable temperature gradients in exo-endothermic reactions; therefore, the catalysts used for the existing and innovative high-energy catalytic processes must meet severe requirements. The catalytic processes in fixed bed reactors are rather complicated and usually include the chemical reactions, the processes of mass and heat transfer and reactant adsorption/desorption. As a result, a specially organised catalytic fixed bed with non-uniform properties (gradient catalysts) may appear more appropriate in some cases than the uniform one. At present, the ideas of gradient catalysts are used for creation the new type of after-burning catalysts, for microchannel reactors. In the theoretical investigation the attention is being increasingly focused on the complex approach based on the optimisation of heat and mass transfer and of the activity of the whole catalyst bed through the optimal bed packing, granule shape, distribution of the active component, heat conductivity etc., i.e. through creation of some optimal gradient medium for conducting the catalytic process. Fundamentals for optimisation of the spatial bed structure, in particular for optimisation of the active component distribution through the bed length, are developed intensively with regard to synthesis of new materials and creation of new methods for arranging reaction beds (for example, in microchannel reactors). The authors of the present book are the first who propose to use the variational approach for solving these problems, so they theoretically formulated the problem of a catalytic process optimisation by means of non-uniform spatial active sites distribution and obtained the analytic solutions for several cases