One of the most important unifying concepts of pure mathematics, that of a vector space, is introduced in this unit. This consists of a set of elements called vectors, which need not be geometric vectors, and two operations, addition of vectors and multiplication by a scalar. The unit looks at examples of vector spaces, and introduces the ideas of bases, dimension, subspace and orthogonal bases.One subsection is intended to be studied in conjunction with an audio, available in the Linear Algebra Block Pack (order code M208/MMPLA).