Linear Algebra is one of the most widely used topics in the mathematical sciences. In the course of Linear Algebra we learnt standard techniques for basic linear algebra tasks including the solution of linear systems, finding eigenvalues/eigenvectors and orthogonalisation of bases. However, these techniques are usually computationally too intensive to be used for the large matrices encountered in practical applications. This course will focus on the fundamental concepts of numerical linear algebra introducing the practical issues to practical applications. It will teach you how to analyze and apply certain algorithms in a reliable and computationally efficient way. We will focus on the following: direct and iterative methods for solving simultaneous linear equations; matrix factorization, decomposition, and transformation; conditioning, stability and efficiency; computation of eigenvalues and eigenvectors. Since many real world problems ultimately reduce to linear algebra concepts and algorithms, there will be a strong emphasis on understanding the advantages and disadvantages, and the limits of applicability for all the covered techniques.