From the contents: Part I Control Applications of Polynomial Positivity Control Applications of Sum of Squares Programming; Analysis of Non-polynomial Systems Using the Sum of Squares Decomposition; A Sum-of-Squares Approach to Fixed-Order H8-Synthesis; LMI Optimization for Fixed-Order H8 Controller Design; An LMI-based Technique for Robust Stability Analysis of Linear Systems with Polynomial Parametric Uncertainties; Stabilization of LPV Systems.- Part II Algebraic Approaches to Polynomial Positivity on the Equivalence of Algebraic Approaches to the Minimization of Forms on the Simplex; Moment Approach to Analyze Zeros of Triangular Polynomial Sets; Polynomials Positive on Unbounded Rectangles; Stability of Interval Two-Variable Polynomials and Quasipolynomials via Positivity.- Part III Numerical Aspects of Polynomial Positivity: Structures, Algorithms, Software Tools Exploiting Algebraic Structure in Sum of Squares Programs.