In these lectures, I will describe numerical methods for various aspects of nonlinear wave computations such as evolution simulation, computation of solitary wave solutions, and computation of linear-stability spectra of solitary waves. On evolution simulation, I will introduce the pseudo-spectral method, the split-step method and the integrating-factor method. On computation of solitary waves, I will introduce the accelerated imaginary-time evolution method, the squared-operator iteration method and the Petviashvili method. Iteration methods for linear-stability eigenvalues of solitary waves will also be presented. Many of these methods were developed only recently. The common features of these methods are their high accuracy, high speed, general applicability, and more importantly, easy implementation. Sample matlab codes of each method will be displayed. The first lecture will be primarily on evolution simulation methods, the second lecture primarily on computation of solitary waves, and the third lecture on eigenvalue computations.