A general formulation of the critical reactor equations is made to include space and velocity variation; the noncritical reactor is treated by using the effective multiplication factor. Two methods are developed for solving the general equation by splitting it into a pair of simultaneous equations: the space-energy split and the fission source split. By using unit sources one equation can be inverted to obtain a pair of integral equations for iterative solution of the general equation. The meaning of neutron importance and the physical picture associated with the concept are given. By using its physical meaning the importance balance equation, which is adjoint to the neutron flux equation, is derived by several methods. Neutron importance is used to formulate the change in reactor power produced by a change in reactor parameters. The effective multiplication factor and reactivity are introduced; the perturbation equation for reactor power change is developed in terms of reactivity. The necessary assumptions to derive the diffusion approximation are given, and the general diffusion equation with continuous energy dependence is obtained. From this the multigroup diffusion equations can be obtained, including the multigroup diffusion perturbation equations. The same methods used for the general critical reactor equation are applied to the diffusion equation to obtain its solution by splitting it into a pair of coupled integral equations. The integral equation for the effective multiplication factor is developed in terms of the fission source variable, and a stationary variational formula obtained for estimating the effective multiplication factor.