This book begins with the history of TLM, an introduction to the theory using mechanical engineering concepts, and the electromagnetic basics of TLM. The authors then demonstrate the theory for use in acoustic propagation, along with examples of MATLAB code. The remainder of the book explores the application of TLM to problems in mechanics, specifically heat and mass transfer, elastic solids, simple deformation models, hydraulic systems, and computational fluid dynamics. A discussion of state-of-the-art techniques concludes the book, offering a look at the current research undertaken by the authors and other leading experts to overcome the limitations of TLM in applying the method to diverse types of systems.