I. Polynomials and Chebyshev Spaces.- 1. Interpolation by Chebyshev Spaces.- 1.1. Lagrange Interpolation by Chebyshev Spaces.- 1.2. Hermite Interpolation by Extended Chebyshev Spaces.- 1.3. Characterization of Extended Complete Chebyshev Spaces.- 1.4. Further Properties of Chebyshev Spaces.- 1.5. Variation Diminishing Property of Order Complete Chebyshev Spaces.- 2. Interpolation by Polynomials and Divided Differences.- 2.1. Divided Differences.- 2.2. Newton Form of Interpolating Polynomials.- 2.3. Nearly Optimal Interpolation Points.- 3. Best Uniform Approximation by Chebyshev Spaces.- 3.1. Best Approximation in Normed Linear Spaces.- 3.2. Characterization of Best Uniform Approximations.- 3.3. Global Unicity and Strong Unicity of Best Uniform Approximations.- 3.4. Algorithm.- 3.5. Approximation Power of Polynomials.- 4. Best L1-Approximation by Chebyshev Spaces.- 4.1. Global Unicity of Best L1-Approximations.- 4.2. Interpolation at Canonical Points.- 5. Best One-Sided L1-Approximation by Chebyshev Spaces and Quadrature Formulas.- 5.1. Unicity of Best One-Sided L1-Approximations.- 5.2. Gauss Quadrature Formulas for Chebyshev Spaces.- 6. Best L2-Approximation.- II. Splines and Weak Chebyshev Spaces.- 1. Weak Chebyshev Spaces.- 1.1. Basic Properties.- 1.2. Best Uniform Approximation by Weak Chebyshev Spaces.- 1.3. Spline Spaces.- 2. B-Splines.- 2.1. Basic Properties.- 2.2. B-Spline Basis.- 2.3. Recurrence Relations.- 2.4. Variation Diminishing Property.- 3. Interpolation by Splines.- 3.1. Lagrange and Hermite Interpolation by Splines.- 3.2. Interpolation by Complete Splines, Periodic Splines and Natural Splines.- 3.3. Quasi-Interpolation.- 4. Best Uniform Approximation by Splines.- 4.1. Characterization, Unicity and Strong Unicity of Best Uniform Approximations.- 4.2. Algorithm (Fixed Knots).- 4.3. Algorithm (Free Knots).- 4.4. Approximation Power of Splines.- 5. Continuity of the Set Valued Metric Projection for Spline Spaces….- 5.1. Upper Semi continuity.- 5.2. Lower Semi continuity.- 5.3. Continuous Selections.- 6. Best L1-Approximation by Weak Chebyshev Spaces.- 6.1. Unicity of Best L1-Approximations.- 6.2. Interpolation at Canonical Points.- 7. Best One-Sided L1-Approximation by Weak Chebyshev Spaces and Quadrature Formulas.- 7.1. Unicity of Best One-Sided L1-Approximations.- 7.2. Gauss Quadrature Formulas for Weak Chebyshev Spaces.- 8. Approximation of Linear Functionals and Splines.- 9. Spaces of Splines with Multiple Knots.- 1. Splines with Free Knots.- 2. Splines in Two Variables.- 2.1. Tensor Product and Blending.- 2.2. Finite Element Functions.- 2.3. Spline Functions.- 3. Spline Collocation and Differential Equations.- References.
