This book provides a balanced selection of both conventional optimization algorithms and modern metaheuristic methods commonly used in mathematical optimization. Conventional algorithms include gradient-based methods such as the steepest descent method, the simplex method for linear programming, Lagrange multipliers, and Hooke-Jeeves pattern search. Metaheuristic methods include ant colony optimization (ACO), particle swarm optimization (PSO), simulated annealing (SA), and Tabu search, recursive method for multiobjective optimization. With dozens of worked examples and three Matlab/Octave programs, this book can ideally serve as a textbook, especially suitable for undergraduates and graduates.