Research in inverse problems have grown significantly over the last 40 years, and engineers no longer have only trial-and-errors methods at their disposal for solving some of their most challenging questions. This handbook brings together a variety of techniques for solving inverse problems, presented by experts in a succinct form suitable for implementation into computer algorithms. It introduces the material with methods for parameter estimation problems, which builds a bridge to the boundary function estimation problem. The methods include sequential function estimation, mollification and space marching techniques, adjoint methods, and gradient-based solution methods.