The text covers the theoretical part of the Linear Algebra course, following the way it is presented in the Bilingual Group of the Degree in Telecommunication Technologies at the University of Alcala. The contents are introduced in a rigorous way, and are motivated by means of problems related to Telecommunications and Applied Mathematics. The usual topics in a Linear Algebra course (systems of linear equations, vector spaces, linear mappings, diagonalization, Euclidean spaces) are addressed here, together with an additional lesson on Boolean algebra, of great interest in Computer Science and Telecommunications.