Some of the more recent theoretical and computational developments in non-linear programming are surveyed. The notions of Lagrange multipliers and duality are discussed together with applications of these ideas to scientific and business problems. Moreover, several algorithms for solving quadratic programming problems are reviewed. Explicit rules are given for two of these algorithms, and a simple example is solved by both methods. A large step gradient method for the solution of convex programs is given and one of Gomory's algorithms for integer programming is described. Simple examples are solved using both of these techniques. Linear fractional programming is also discussed briefly.