George Collins discovery of Cylindrical Algebraic Decomposition (CAD) as a method for Quantifier Elimination (QE) for the elementary theory of real closed fields brought a major breakthrough in automating mathematics with recent important applications in high-tech areas (e.g. robot motion), also stimulating fundamental research in computer algebra over the past three decades. This volume is a state-of-the art collection of important papers on CAD and QE and on the related area of algorithmic aspects of real geometry. In addition to original contributions by S. Basu et al., L. Gonzalez-Vega et al., G. Hagel, H. Hong and J.R. Sendra, J.R. Johnson, S. McCallum, D. Richardson, and V. Weispfenning and a survey by G.E. Collins outlining the twenty-year progress in CAD-based QE it brings together seminal publications from the area: A. Tarski: A Decision Method for Elementary Algebra and Geometry G.E. Collins: Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition M.J. Fischer and M.O. Rabin: Super-Exponential Complexity of Presburger Arithmetic D.S. Arnon et al.: Cylindrical Algebraic Decomposition I: The Basic Algorithm; II: An Adjacency Algorithm for the Plane H. Hong: An Improvement of the Projection Operator in Cyclindrical Algebraic Decomposition G.E. Collins and H. Hong: Partial Cylindrical Algebraic Decomposition for Quantifier Elimination H. Hong: Simple Solution Formula Construction in Cylindrical Algebraic Decomposition Based Quantifier Elimination J. Renegar: Recent Progress on the Complexity of the Decision Problem for the Reals