This book describes and applies methods for the solution of problems on the energy and time dependent behaviour of either neutrons or photons in systems with arbitrarily complex shapes and compositions. Solutions and precise gauges are provided for both global and local accuracy of solutions and it is shown that this new and deterministic method is a valuable complementary tool to the stochastic Monte Carlo Method. Assuming no previous knowledge of finite element methods or transport theory, the reader is taken to the frontiers of research where many diverse applications of the methods are opening up in non-nuclear fields. The theory is illustrated in depth for both test problems and problems that arise in practical situations in the fields of nuclear power and mineral prospecting. The methods described are also applicable to infra-red medical tomography, and to environmental problems such as the response of clouds and vegetation to the sun"s rays.