Chapter 11. Computing All Solutions to Polynomial Equations in Economics Multiplicity of equilibria is a common problem in many economic models. In general it is impossible to devise methods that always find all equilibria for any type of model. A notable exception are models in which all equilibria are solutions to a system of polynomial equations since there are powerful solution methods for finding all solutions to such polynomial systems. In many economic applications equilibria can indeed be characterized as solutions to a system of polynomial equations. This handbook article provides a hands on introduction to two solution methods for finding all solutions to polynomial systems; the first approach relies on Gröbner bases the second approach employs all solution homotopy methods. Several economic examples show how to compute all equilibria using modern software implementations of these two methods.