Nonlinear equations come to us in tremendous variety, each with its own questions and its own difficulties. At one extreme are the completely integrable equations, with constants of the motion and a rich algebraic structure. At the other extreme is chaos, with turbulent solutions and statistical averages. Between these two possibilities, algebraic and ergodic, lies the full range of nonlinear phenomena. There are smooth solutions which develop shocks, or bifurcate, or maintain slow and nearly periodic variations that imitate the linear theory. Each of these questions requires a separate treatment, and the subject would be simpler if we know for every equation which behavior to expect.