Computation of Real Radicals of Polynomial Ideals -- Semialgebraic geometry of polynomial control problems -- The Resultant via a Koszul Complex -- Grรถbner Bases and Standard Monomial Theory -- A Continuous and rational solution to Hubertโ{128}{153}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-Levineโ{128}{153}s theorem to real algebraic geometry -- Applications of Algebraic Geometry to Computer Vision -- Disproving Hibiโ{128}{153}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 Grรถbner Bases -- Complexity of Bezoutโ{128}{153}s Theorem II: Volumes and Probabilities -- A Parametrized Nullstellensatz -- An Elimination Method Based on Seidenbergโ{128}{153}s Theory and Its Applications