Computation of Real Radicals of Polynomial Ideals.- Semialgebraic geometry of polynomial control problems.- The Resultant via a Koszul Complex.- Gröbner Bases and Standard Monomial Theory.- A Continuous and rational solution to Hubert's 17th problem and several cases of the Positivstellensatz.- The analytic spread of the ideal of a monomial curve in projective 3-space.- Computational Complexity of Sparse Real Algebraic Function Interpolation.- Shade, Shadow and Shape.- Arrangements of singularities and proper partitions of Dynkin diagrams.- Versal deformations of powers of volume forms.- Computing subfields: Reverse of the primitive element problem.- Applications of Eisenbud-Levine's theorem to real algebraic geometry.- Applications of Algebraic Geometry to Computer Vision.- Disproving Hibi's Conjecture with CoCoA or Projective Curves with bad Hilbert Functions.- Counting real zeros in the multivariate case.- Finding the number of distinct real roots of sparse polynomials of the form p(x, xn).- Locally effective objects and algebraic topology.- Decision of Algebra Isomorphisms using Gröbner Bases.- Complexity of Bezout's Theorem II: Volumes and Probabilities.- A Parametrized Nullstellensatz.- An Elimination Method Based on Seidenberg's Theory and Its Applications.