An introduction to linear algebra, mainly in R^n but concluding with an introduction to abstract vector spaces. The principal topics are vectors, systems of linear equations, matrices, eigenvalues and eigenvectors and orthogonality. The important notions of linear independence, span and bases are introduced. This course is both a preparation for the practical use of vectors, matrices and systems of equations and also lays the groundwork for a more abstract, pure-mathematical treatment of vector spaces. Students will learn how to use a computer to calculate the results of some simple matrix operations and to visualise vectors.