This book delves deeply into the real-world technologies behind the 'directed energy weapons' that many believe exist only within the confines of science fiction. On the contrary, directed energy weapons such as high energy lasers are very real, and this book provides a crash course in all the physical and mathematical concepts that make these weapons a reality. Written to serve both scientists researching the physical phenomena of laser effects, as well as engineers focusing on practical applications, the author provides worked examples demonstrating issues such as how to solve for heat diffusion equation for different boundary and initial conditions. Several sections are devoted to reviewing and dealing with solutions of diffusion equations utilizing the aid of the integral transform techniques. Ultimately this book examines the state-of-the-art in currently available high energy laser technologies, and suggests future directions for accelerating practical applications in the field.