| Preface | p. xi |
| Preface to the 3rd Edition | p. xv |
| Introduction | p. 1 |
| Approximation Problems | p. 1 |
| Polynomials | p. 2 |
| Piecewise Polynomials | p. 3 |
| Spline Functions | p. 5 |
| Function Classes and Computers | p. 7 |
| Historical Notes | p. 9 |
| Preliminaries | p. 12 |
| Function Classes | p. 12 |
| Taylor Expansions and the Green's Function | p. 14 |
| Matrices and Determinants | p. 19 |
| Sign Changes and Zeros | p. 24 |
| Tchebycheff Systems | p. 29 |
| Weak Tchebycheff Systems | p. 36 |
| Divided Differences | p. 45 |
| Moduli of Smoothness | p. 54 |
| The K-Functional | p. 59 |
| n-Widths | p. 70 |
| Periodic Functions | p. 75 |
| Historical Notes | p. 76 |
| Remarks | p. 79 |
| Polynomials | p. 83 |
| Basic Properties | p. 83 |
| Zeros and Determinants | p. 85 |
| Variation-Diminishing Properties | p. 89 |
| Approximation Power of Polynomials | p. 91 |
| Whitney-Type Theorems | p. 97 |
| The Inflexibility of Polynomials | p. 101 |
| Historical Notes | p. 103 |
| Remarks | p. 105 |
| Polynomial Splines | p. 108 |
| Basic Properties | p. 108 |
| Construction of a Local Basis | p. 112 |
| B-Splines | p. 118 |
| Equally Spaced Knots | p. 134 |
| The Perfect B-Spline | p. 139 |
| Dual Bases | p. 142 |
| Zero Properties | p. 154 |
| Matrices and Determinants | p. 165 |
| Variation-Diminishing Properties | p. 177 |
| Sign Properties of the Green's Function | p. 180 |
| Historical Notes | p. 181 |
| Remarks | p. 185 |
| Computational Methods | p. 189 |
| Storage and Evaluation | p. 189 |
| Derivatives | p. 195 |
| The Piecewise Polynomial Representation | p. 197 |
| Integrals | p. 199 |
| Equally Spaced Knots | p. 204 |
| Historical Notes | p. 207 |
| Remarks | p. 208 |
| Approximation Power of Splines | p. 210 |
| Introduction | p. 210 |
| Piecewise Constants | p. 212 |
| Piecewise Linear Functions | p. 220 |
| Direct Theorems | p. 223 |
| Direct Theorems in Intermediate Spaces | p. 233 |
| Lower Bounds | p. 236 |
| n-Widths | p. 239 |
| Inverse Theory for p = [infinity] | p. 240 |
| Inverse Theory for 1 < p < [infinity] | p. 252 |
| Historical Notes | p. 261 |
| Remarks | p. 264 |
| Approximation Power of Splines (Free Knots) | p. 268 |
| Introduction | p. 268 |
| Piecewise Constants | p. 270 |
| Variational Moduli of Smoothness | p. 276 |
| Direct and Inverse Theorems | p. 278 |
| Saturation | p. 283 |
| Saturation Classes | p. 286 |
| Historical Notes | p. 293 |
| Remarks | p. 294 |
| Other Spaces of Polynomial Splines | p. 297 |
| Periodic Splines | p. 297 |
| Natural Splines | p. 309 |
| g-Splines | p. 316 |
| Monosplines | p. 330 |
| Discrete Splines | p. 342 |
| Historical Notes | p. 360 |
| Remarks | p. 362 |
| Tchebycheffian Splines | p. 363 |
| Extended Complete Tchebycheff Systems | p. 363 |
| A Green's Function | p. 373 |
| Tchebycheffian Spline Functions | p. 378 |
| Tchebycheffian B-Splines | p. 380 |
| Zeros of Tchebycheffian Splines | p. 388 |
| Determinants and Sign Changes | p. 390 |
| Approximation Power of T-Splines | p. 393 |
| Other Spaces of Tchebycheffian Splines | p. 395 |
| Exponential and Hyperbolic Splines | p. 405 |
| Canonical Complete Tchebycheff Systems | p. 407 |
| Discrete Tchebycheffian Splines | p. 411 |
| Historical Notes | p. 417 |
| L-Splines | p. 420 |
| Linear Differential Operators | p. 420 |
| A Green's Function | p. 424 |
| L-Splines | p. 429 |
| A Basis of Tchebycheffian B-Splines | p. 433 |
| Approximation Power of L-Splines | p. 438 |
| Lower Bounds | p. 440 |
| Inverse Theorems and Saturation | p. 444 |
| Trigonometric Splines | p. 452 |
| Historical Notes | p. 459 |
| Remarks | p. 461 |
| Generalized Splines | p. 462 |
| A General Space of Splines | p. 462 |
| A One-Sided Basis | p. 466 |
| Constructing a Local Basis | p. 470 |
| Sign Changes and Weak Tchebycheff Systems | p. 472 |
| A Nonlinear Space of Generalized Splines | p. 478 |
| Rational Splines | p. 479 |
| Complex and Analytic Splines | p. 480 |
| Historical Notes | p. 482 |
| Tensor-Product Splines | p. 484 |
| Tensor-Product Polynomial Splines | p. 484 |
| Tensor-Product B-Splines | p. 486 |
| Approximation Power of Tensor-Product Splines | p. 489 |
| Inverse Theory for Piecewise Polynomials | p. 492 |
| Inverse Theory for Splines | p. 497 |
| Historical Notes | p. 499 |
| Some Multidimensional Tools | p. 501 |
| Notation | p. 501 |
| Sobolev Spaces | p. 503 |
| Polynomials | p. 506 |
| Taylor Theorems and the Approximation Power of Polynomials | p. 507 |
| Moduli of Smoothness | p. 516 |
| The K-Functional | p. 520 |
| Historical Notes | p. 521 |
| Remarks | p. 523 |
| Supplement | p. 524 |
| References | p. 534 |
| New References | p. 559 |
| Index | p. 577 |
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