This text develops a repertoire of analytical tools related to linear spaces, linear transformations, and linear systems, providing students with the facility to investigate new theoretical concepts in several engineering specialties. Also described are a variety of applications, with examples cited throughout the book. The emphasis is on general cases which illustrate basic principles. Carefully chosen special cases are then deduced from them, which further illustrate the main results. Each result is stated as a logical proposition, with proofs which help establish significant techniques. Included are numerous pictorial representations that supplement the topics discussed.