This course introduces the principal algorithms for linear, network, discrete, nonlinear, dynamic optimization and optimal control. Emphasis is on methodology and the underlying mathematical structures. Topics include description of the problem of optimisation and the geometry of Rn, n > 1, convex sets and convex functions, unconstrained optimization: necessary and sufficient conditions for local minima/maxima,  constrained optimization: equality and inequality constraints, Lagrange multipliers and the Kuhn-Tucker conditions, computational methods  for unconstrained and constrained optimization, steepest descent and Newton's methods, quadratic programming, penalty and barrier methods, sequential quadratic programming (SQP) implementation in MATLAB/OCTAVE.