This textbook was designed for senior undergraduates in mathematics, engineering and the sciences with diverse backgrounds and goals. It presents modern tools from numerical linear algebra with supporting theory along with examples and exercises, both theoretical and computational with MATLAB. The major topics of numerical linear algebra covered are direct methods for solving linear systems, iterative methods for large and sparse systems (including the conjugate gradient method) and eigenvalue problems. Basic linear algebra (of the type taken in the engineering curriculum) is assumed. Further matrix theory is developed in a self-contained way when needed to expalin why methods work and how they might fail. This book is intended for a one term course for undergraduate students in applied and computational mathematics, the sciences, engineering, computer science, financial mathematics and actuarial science. It is also a good choice for a beginning graduate level course for students who will use the numerical methods to solve problems in their own areas.