This book is written for undergraduate students in engineering and materials science and is meant to be an introductory course in linear algebra and vector calculus. The book contains many examples of application of the methods to problems taken from courses taught in the curriculum of structural engineering and mechanical engineering, in particular, as well as other branches of engineering. Several themes are used throughout including applications to the theory of deformation of solids and the dynamics of structures. These examples are designed to illustrate to the reader the applicability of the methods of linear algebra to Òreal lifeÓ engineering problems.