Contents include: On Jackson`s Inequalities for Approximations in L2 of Periodic Functions by Trigonometric Polynomials and of Functions on the Line by Entire Functions. The Olovyanishnikov Inequality for Multivariate Functions. Bernstein-Durrmeyer Type Quasi-Interpolants on Intervals. Adaptive Approximation of Curves. An Efficient Definition of the Divided Difference. Extended Cubature Formula of Turan Type (0,2) for the Ball, The Multivariate Fundamental Theorem of Algebra, Bezout`s Theorem and Nullstellensatz, Canonical Point Sets for Best One-Sided L1-Approximation by Quasi-Blending Functions, A Characterization Theorem for the K-functional for Kantorovich and Durrmeyer Operators, Some Error Estimates in Learning Theory, B-Spaces and their Characterization via Anistropic Franklin Bases. On Optimal Recovery of Heat Equation Solutions; Markov`s Inequalities in Integral Norm for Oscillating Weighted Polynomials. Standard and non-standard quadratures of Gaussian Type; Inequalities for Real-Root Polynomials. On Smooth Interpolation. Thoughts over the Smale`s Mean Value Conjecture. Twelve Proofs of the Markov Inequality. New Technique for Error Analysis of Finite Element Approximations of Parabolic Problems with Non-Smooth Initial Data. On Generalized Tractability for Multivariate Problems. On Polynomial Interpolation on the Unit Ball.