Abstract: Computational real algebraic geometry studies various algorithmic questions dealing with the real solutions of a system of equalities, inequalities, and inequations of polynomials over the real numbers. This emerging field is largely motivated by the power and elegance with which it solves a broad and general class of problems arising in robotics, vision, computer aided design, geometric theorem proving, etc.

The following survey paper discusses the underlying concepts, algorithms and a series of representative applications. This paper will appear as a chapter in the "Handbook of Discrete and Computational Geometry" (Edited by J.E. Goodman and J. O'Rourke), CRC Series in Discrete and Combinatorial Mathematics.