The remote sensing of earth from space is a nonlinear problem of estimating physical parameters from measurements. From an analytical point of view, it is a case of radiative transfer in inhomogeneous plane-parallel and spherical media. This book provides a modern treatment of both direct and inverse problems applicable to the remote sensing of earth from space or from the air. Starting from a physical description of the process, the authors develop innovative mathematical models, fundamental mathematics for the analysis of these models, and methods for obtaining computational solutions. Also featured are the results of recent research using this approach. For example, invariant imbedding techniques, associative memory artificial neural networks, and the automatic evaluation of derivatives have been used to solve inverse problems. This book covers uniform parallel illumination, internal sources, and incident spotlight beams, making it indispensable for researchers working to reduce the atmospheric distortion of remotely sensed terrestrial images.