Inroduction. Round off error analysis. Direct methods for solving linear systems (elimination methods, factorization). Iterative methods for solving linear systems, Semi-Iterative methods. The Conjugate Gradient method. Numerical computation of eigenvalues and eigenvectors: iterative methods (Power method), Transformation methods (Jacobi, Givens, Householder, LR, QR). Introduction to the numerical solution of partial differential equations.