In the previous chapters we have focussed on matrices and their properties. We have defined algebraic operations with matrices and derived important concepts associated with them, including their rank, determinant, characteristic polynomial, and eigenvalues. In this chapter we place these concepts in a more abstract framework by introducing the idea of a vector space. Matrices form one of the most important examples of vector spaces, and properties of certain (namely, finite dimensional) vector spaces can be studied in a transparent way using matrices. In the next chapter we will study (linear) maps between vector spaces, and there the connection with matrices will play a central role as well.