Many practical scientific and engineering problems are functions of multiple variables, which are systematically organized into a system of linear equations. The objective is then to solve the equations simultaneously. If the system is nonlinear, however, it may be always approximated to the first-order equations; therefore, the methods of linear algebra are almost universally applicable across scientific disciplines. Exercises given in this chapter illustrate some of the most typical definitions, forms, and techniques assumed to be in the repertoire of engineering and scientific students. Obviously, the scope of this single chapter is much too small to completely cover all details of this immense branch in mathematics; nevertheless, it serves as the solid introduction to the basics of linear algebra.