Linear algebra is a vital course for students. Few subjects can claim to have such widespread applications in other areas of mathematics-multi variable calculus, differential equations, probability, and in physics, biology, chemistry, economics, finance, psychology, sociology. and all fields of engineering. It also presents the students with an excellent opportunity to learn how to deal with abstract concepts. This module introduces the basic ideas and computational techniques of linear algebra. It also includes a wide variety of carefully selected applications. It also introduces the students to working with abstract concepts. Finally, in covering the basic ideas of linear algebra, the abstract ideas are carefully balanced by a considerable emphasis on the geometrical and computational aspects of the subject. Throughout this module, a great variety of examples and exercises of the important concepts are included. The study of such examples is of fundamental importance. It tends to minimize the number of students who can repeat definition, theorem, and proof logically without grasping the meaning of the abstract concepts. Assessments are also included in every section of this module to measure the students' learning as to how far they have learned the concepts. Finally, answers on exercises are provided for the students to answer the assessments. As with the rest of the book, the exercises and assessments aim to buildability and help students experience the pleasure of doing mathematics. Students should see how the ideas arise and should be able to picture themselves doing the same type of work.