| Acknowledgments | |
| Preface | |
| Biographical sketches | p. 1 |
| Curriculum vitae | p. 1 |
| Felix Hausdorff: mathematician, philosopher, poet | p. 5 |
| Author's reflections | p. 24 |
| References: the works of Felix Hausdorff | p. 37 |
| References to the biographical notes | p. 43 |
| The paradox of the sphere | p. 45 |
| Hausdorff's decomposition of the sphere | p. 46 |
| The Banach-Tarski paradox | p. 58 |
| Non-measurable sets in R[superscript 1] and R[superscript 2] | p. 61 |
| Exotic measures and the problem of Ruziewicz | p. 69 |
| Group theoretic implications of the Hausdorff theorem | p. 71 |
| A fixed point view on paradoxical decompositions | p. 80 |
| Inaccessible numbers and the hierarchal structure of set theory | p. 94 |
| The infinite number of Cantor's set theory | p. 95 |
| Hausdorff's weakly inaccessible cardinals and a certain set-theoretic alpinism | p. 117 |
| The axioms of Zermelo and Fraenkel and their paradoxical background | p. 127 |
| The Godel theorem and the cumulative hierarchy of sets | p. 141 |
| On the continuum hypothesis and related problems | p. 167 |
| The conditions of the existence and non-existence of non-measurable sets | p. 188 |
| Cantor, Hausdorff and Godel's pyramid of paradoxes | p. 197 |
| The Godel theorem and a certain mathematical catastrophism | p. 203 |
| Hausdorff's intuitions versus present-day mathematics | p. 205 |
| The Hausdorff measures, Hausdorff dimensions and fractals | p. 219 |
| The Hausdorff measure and dimension | p. 221 |
| The standard example of the Cantor set | p. 231 |
| Ephemeral sets of strong measure zero | p. 234 |
| The implications in number theory | p. 236 |
| The Hausdorff dimension of the Cartesian product of sets | p. 239 |
| The Hausdorff-Besicovitch dimension versus Hausdorff operations | p. 241 |
| Metric spaces | p. 245 |
| The Hausdorff topology and topological stable dimension | p. 250 |
| The Hausdorff-Besicovitch dimension versus the topological dimension | p. 272 |
| The coefficient [actual symbol not reproducible], that is, the topological measure of Borsuk | p. 276 |
| The concept of fractals | p. 278 |
| One flew over the land of fractals | p. 281 |
| The phenomenon of self-similarity | p. 367 |
| Multifractals | p. 375 |
| Natural fractals | p. 384 |
| The Olbers paradox and fractal approaches to cosmology | p. 391 |
| Fractals: illusion, speculation or mathematics? | p. 397 |
| The Baker-Campbell-Hausdorff formula | p. 414 |
| The Hausdorff series | p. 415 |
| A continuous Baker-Campbell-Hausdorff problem | p. 433 |
| The problem of the convergence of the Hausdorff series | p. 439 |
| Lie algebras, Lie groups and the BCH theorem | p. 443 |
| Lie superalgebras | p. 463 |
| The BCH formula for Lie superalgebras | p. 475 |
| A discussion about Lie supergroups defined via the BCH formula | p. 488 |
| Examples | p. 497 |
| What sort of things are superfractals? | p. 511 |
| Superbundles formed by means of the BCH formula | p. 514 |
| What is a first super Chern class? | p. 519 |
| Grassmann structures for "extrinsic" supergeometries | p. 521 |
| Super Lie groups, that is, supergroups in the sense of Berezin and Alice Rogers | p. 536 |
| Graded Lie groups, that is, Lie supergroups in the sense of Kostant and Berezin | p. 548 |
| What sort of supergroups are the best? | p. 553 |
| Hausdorff matrices | p. 566 |
| The Holder, Cesaro and Hausdorff means | p. 567 |
| The Toeplitz theorem | p. 573 |
| The regularity and equivalency conditions for Hausdorff matrices | p. 576 |
| Essential Hausdorff cores of certain infinite sequences | p. 593 |
| The generalizations of the Hausdorff summation | p. 597 |
| Solitons and soliton equations | p. 610 |
| An outline of the inverse scattering method | p. 617 |
| The direct method of Hirota | p. 623 |
| Periodic solutions of the KdV equation and related problems | p. 633 |
| Hausdorff's other results in classical, spectral and harmonic analysis | p. 647 |
| Appendix | p. 667 |
| References | p. 688 |
| Addendum | p. 691 |
| Hints to problems | p. 699 |
| Notation | p. 701 |
| Index of authors and subjects | p. 707 |
| Index of paradoxes | p. 735 |
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