0 Introduction.- 1 Algebraically Closed Fields.- 2 Real Closed Fields.- 3 Semi-Algebraic Sets.- 4 Algebra.- 5 Decomposition of Semi-Algebraic Sets.- 6 Elements of Topology.- 7 Quantitative Semi-algebraic Geometry.- 8 Complexity of Basic Algorithms.- 9 Cauchy Index and Applications.- 10 Real Roots.- 11 Polynomial System Solving.- 12 Cylindrical Decomposition Algorithm.- 13 Existential Theory of the Reals.- 14 Quantifier Elimination.- 15 Computing Roadmaps and Connected Components of Algebraic Sets.- 16 Computing Roadmaps and Connected Components of Semi-algebraic Sets.- References.
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