Functions between sets, or Maps, are the working tools of the mathematician. In this section we will investigate maps between vector spaces. In particular we will focus on linear maps, and we will see that linear maps may be used to solve many types of problems in mathematics including dynamical systems and Markov processes. In particular we will discover that every linear map between vector spaces may be represented by a matrix. This is the fourth abstraction, and it will allow us to analyse linear maps by their matrix representation. Further on in the course, we will discover that the "essential" characteristics of linear transformations may be represented by special or canonical forms of matrices.