| Introduction | p. xi |
| Acknowledgments | p. xv |
| Notation and General Definitions | p. xvii |
| Examples of Group Actions on the Circle | p. 1 |
| The Group of Rotations | p. 1 |
| The Group of Translations and the Affine Group | p. 2 |
| The Group PSL(2, ) | p. 4 |
| PSL(2, ) as the Möbius group | p. 4 |
| PSL(2, ) and the Liouville geodesic current | p. 7 |
| PSL(2, ) and the convergence property | p. 9 |
| Actions of Lie Groups | p. 11 |
| Thompson's Groups | p. 12 |
| Thurston's piecewise projective realization | p. 15 |
| Ghys-Sergiescu's smooth realization | p. 18 |
| Dynamics of Groups of Homeomorphisms | p. 23 |
| Minimal Invariant Sets | p. 23 |
| The case of the circle | p. 23 |
| The case of the real line | p. 29 |
| Some Combinatorial Results | p. 30 |
| Poincaré's theory | p. 30 |
| Rotation numbers and invariant measures | p. 37 |
| Faithful actions on the line | p. 39 |
| Free actions and Hölder's theorem | p. 43 |
| Translation numbers and quasi-invariant measures | p. 49 |
| An application to amenable, orderable groups | p. 58 |
| Invariant Measures and Free Groups | p. 63 |
| A weak version of the Tits alternative | p. 63 |
| A probabilistic viewpoint | p. 69 |
| Dynamics of Groups of Diffeomorphisms | p. 80 |
| Denjoy's Theorem | p. 80 |
| Sacksteder's Theorem | p. 90 |
| The classical version in class | p. 91 |
| The version for pseudogroups | p. 96 |
| A sharp version via Lyapunov exponents | p. 103 |
| Dummy's First Theorem: On the Existence of Exceptional Minimal Sets | p. 110 |
| The statement of the result | p. 110 |
| An expanding first-return map | p. 112 |
| Proof of the theorem | p. 116 |
| Dummy's Second Theorem: On the Space of Semiexceptional Orbits | p. 119 |
| The statement of the result | p. 119 |
| A criterion for distinguishing two different ends | p. 123 |
| End of the proof | p. 127 |
| Two Open Problems | p. 130 |
| Minimal actions | p. 130 |
| Actions with an exceptional minimal set | p. 141 |
| On the Smoothness of the Conjugacy between Groups of Diffeomorphisms | p. 146 |
| Sternberg's linearization theorem and conjugacies | p. 147 |
| The case of bi-Lipschitz conjugacies | p. 152 |
| Structure and Rigidity via Dynamical Methods | p. 158 |
| Abelian Groups of Diffeomorphisms | p. 158 |
| Kopell's lemma | p. 158 |
| Classifying Abelian group actions in class | p. 164 |
| Szekeres's theorem | p. 165 |
| Denjoy counterexamples | p. 171 |
| On intermediate regularities | p. 182 |
| Nilpotent Groups of Diffeomorphisms | p. 192 |
| The Plante-Thurston Theorems | p. 192 |
| On growth of groups of diffeomorphisms | p. 195 |
| Nilpotence, growth, and intermediate regularity | p. 202 |
| Polycyclic Groups of Diffeomorphisms | p. 209 |
| Solvable Groups of Diffeomorphisms | p. 211 |
| Some examples and statements of results | p. 211 |
| The metabelian case | p. 216 |
| The case of the real line | p. 220 |
| On the Smooth Actions of Amenable Groups | p. 223 |
| Rigidity via Cohomological Methods | p. 226 |
| Thurston's Stability Theorem | p. 226 |
| Rigidity for Groups with Kazhdan's Property (T) | p. 233 |
| Kazhdan's property (T) | p. 233 |
| The statement of the result | p. 240 |
| Proof of the theorem | p. 243 |
| Relative property (T) and Haagerup's property | p. 251 |
| Superrigidity for Higher-Rank Lattice Actions | p. 253 |
| Statement of the result | p. 253 |
| Cohomological superrigidity | p. 256 |
| Superrigidity for actions on the circle | p. 262 |
| Some Basic Concepts in Group Theory | p. 267 |
| Invariant Measures and Amenable Groups | p. 269 |
| References | p. 273 |
| Index | p. 287 |
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