Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Numerical Continuation is a method of computing approximate solutions of a system of parameterized nonlinear equations, F(u,lambda) = 0 The parameter λ is usually a real scalar, and the solution an n-vector. For a fixed parameter value λ,, F(ast,lambda) maps Euclidean n-space into itself. Often the original mapping F is from a Banach space into itself, and the Euclidean n-space is a finite dimensional approximation to the Banach space. A steady state, or fixed point, of a parameterized family of flows or maps are of this form, and by discretizing trajectories of a flow or iterating a map, periodic orbits and heteroclinic orbits can also be posed as a solution of F = 0.