The main goal of the thesis is to solve the inverse problem for REMOTE SENSING of thermal conductivity. For this purpose the following is undertaken - A study of what is REMOTE SENSING ?. –Reduction some problems in REMOTE SENSING to a mathematical inverse problem involving integral equations, or partial or ordinary differential equations, or system of algebraic equations. Some methods for solving mathematical inverse problems are discussed and a computer program for each method is written and implemented to solve some examples. The direct variational method is developed and modified for solving mathematical inverse problems and a computer program, .implementing the method is carried out for the solution of the inverse problem of a one dimensional linear diffusion equation. All results are compared with the .exact solution if is available; these results are given in graphical and tabulated forms.