The introduction of metamaterials and transformation optics has brought the possibilities for manipulating electromagnetic waves to an unprecedented level, suggesting applications like super-resolution imaging, cloaking, subwavelength focusing, and field localization. The refractive index of metamaterial structures in transformation optics typically has to be spatially graded. This paper presents a full analytical method for description of the field propagation through composites with gradient refractive index. The remarkable property of this approach is that it gives explicit general expressions for the field intensity and transmission and reflection coefficients, without reference to any boundary conditions. This opens a possibility for a novel fundamental theory of a number of important electromagnetic phenomena. The method enables calculation of wave propagation parameters within structures with arbitrary losses, arbitrary spectral dispersions, and arbitrary slopes of permittivity and permeability gradients, from mild to abrupt.