This book has been written primarily for students who have a fairly substantial mathematical background. It focuses on teaching students in bioengineering and environmental engineering who have not had such exposure to mathematical concepts.The book: -- Includes practical algorithms on CD-ROM for forward simulation and inversion of wave propagation in 2D.-- Discusses in clear terms the mathematical preliminaries that are required for a proper understanding of the inversion/imaging problem, as they are required.-- Includes careful discussion of the case of acoustic wave propagation in biological tissue (human breast for example). After this introduction, the more difficult cases of electromagnetic waves in non-magnetic media are considered. These require discussion of the vector wave equation, and the numerical methods used in their solution. The methods chosen are the finite difference time domain method, the integral equation method, and the associated hybrid method, which combines the particular advantages of the first two methods.-- Discusses the important case of the diffusion approximation to the EM wave equations, and its many applications. Such applications include: (1) location of buried mines in surf zones, (2) location and delineation of hazardous waste leakage in waste disposal sites (dense nonaqueous phase liquids -- DNAPL's) and (3) u-impedance imaging of cells.