Solving equations, and systems of equations, of all kinds, both algebraic and transcendental, is a very frequent task in a physicist’s life. Very often equations, particularly algebraic nonlinear equations and transcendental equations, have no analytical solutions. In this case we look for approximate numerical solutions. Some equations do not even admit solutions at all, but, of course, we shall not deal this case here! However, when tackling equations we must consider the unlucky possibility that its solution simply does not exist. In this chapter we shall consider the numerical solution of equations and systems of equations not involving the derivatives of the unknowns. Ordinary differential equations are left to Chap.  5 .