The Lanczos Method: Evolution and Application is divided into two distinct parts. The first part reviews the evolution of one of the most widely used numerical techniques in the industry. The development of the method, as it became more robust, is demonstrated through easy-to-understand algorithms. The second part contains industrial applications drawn from the author’s experience. These chapters provide a unique interaction between the numerical algorithms and their engineering applications. This is a valuable reference for numerical analysts and engineers and can be used as a supplementary or reference text at the graduate level. Readers should be familiar with basic linear algebra and numerical analysis.