| Classes of Random Trees | p. 1 |
| Basic Notions | p. 2 |
| Rooted Versus Unrooted trees | p. 2 |
| Plane Versus Non-Plane trees | p. 3 |
| Labelled Versus Unlabelled Trees | p. 3 |
| Combinatorial Trees | p. 4 |
| Binary Trees | p. 5 |
| Planted Plane Trees | p. 6 |
| Labelled Trees | p. 7 |
| Labelled Plane Trees | p. 8 |
| Unlabelled Trees | p. 8 |
| Unlabelled Plane Trees | p. 9 |
| Simply Generated Trees - Galton-Watson Trees | p. 9 |
| Recursive Trees | p. 13 |
| Non-Plane Recursive Trees | p. 13 |
| Plane Oriented Recursive Trees | p. 14 |
| Increasing Trees | p. 15 |
| Search Trees | p. 17 |
| Binary Search Trees | p. 18 |
| Fringe Balanced m-Ary Search Trees | p. 19 |
| Digital Search Trees | p. 21 |
| Tries | p. 22 |
| Generating Functions | p. 25 |
| Counting with Generating Functions | p. 26 |
| Generating Functions and Combinatorial Constructions | p. 27 |
| Pólya's Theory of Counting | p. 33 |
| Lagrange Inversion Formula | p. 36 |
| Asymptotics with Generating Functions | p. 37 |
| Asymptotic Transfers | p. 38 |
| Functional Equations | p. 43 |
| Asymptotic Normality and Functional Equations | p. 46 |
| Transfer of Singularities | p. 54 |
| Systems of Functional Equations | p. 62 |
| Advanced Tree Counting | p. 69 |
| Generating Functions and Combinatorial Trees | p. 70 |
| Binary and m-ary Trees | p. 70 |
| Planted Plane Trees | p. 71 |
| Labelled Trees | p. 73 |
| Simply Generated Trees - Galton-Watson Trees | p. 75 |
| Unrooted Trees | p. 77 |
| Trees Embedded in the Plane | p. 81 |
| Additive Parameters in Trees | p. 82 |
| Simply Generated Trees - Galton-Watson Trees | p. 84 |
| Unrooted Trees | p. 87 |
| Patterns in Trees | p. 90 |
| Planted, Rooted and Unrooted Trees | p. 91 |
| Generating Functions for Planted Rooted Trees | p. 92 |
| Rooted and Unrooted Trees | p. 99 |
| Asymptotic Behaviour | p. 101 |
| The Shape of Galton-Watson Trees and Pólya Trees | p. 107 |
| The Continuum Random Tree | p. 108 |
| Depth-First Search of a Rooted Tree | p. 108 |
| Real Trees | p. 109 |
| Galton-Watson Trees and the Continuum Random Tree | p. 111 |
| The Profile of Galton-Watson Trees | p. 115 |
| The Distribution of the Local Time | p. 118 |
| Weak Convergence of Continuous Stochastic Processes | p. 120 |
| Combinatorics on the Profile of Galton-Watson Trees | p. 125 |
| Asymptotic Analysis of the Main Recurrence | p. 126 |
| Finite Dimensional Limiting Distributions | p. 129 |
| Tightness | p. 134 |
| The Height of Galton-Watson Trees | p. 139 |
| Depth-First Search | p. 149 |
| The Profile of Pólya Trees | p. 154 |
| Combinatorial Setup | p. 154 |
| Asymptotic Analysis of the Main Recurrence | p. 156 |
| Finite Dimensional Limiting Distributions | p. 164 |
| Tightness | p. 168 |
| The Height of Pólya Trees | p. 177 |
| The Vertical Profile of Trees | p. 187 |
| Quadrangulations and Embedded Trees | p. 188 |
| Profiles of Trees and Random Measures | p. 196 |
| General Profiles | p. 196 |
| Space Embedded Trees and ISE | p. 196 |
| The Distribution of the ISE | p. 204 |
| Combinatorics on Embedded Trees | p. 207 |
| Embedded Trees with Increments ±1 | p. 207 |
| Embedded Trees with Increments 0, ±1 | p. 214 |
| Naturally Embedded Binary Trees | p. 216 |
| Asymptotics on Embedded Trees | p. 219 |
| Trees with Small Labels | p. 219 |
| The Number of Nodes of Given Label | p. 225 |
| The Number of Nodes of Large Labels | p. 229 |
| Embedded Trees with Increments 0 and ±1 | p. 235 |
| Naturally Embedded Binary Trees | p. 235 |
| Recursive Trees and Binary Search Trees | p. 237 |
| Permutations and Trees | p. 238 |
| Permutations and Recursive Trees | p. 239 |
| Permutations and Binary Search Trees | p. 246 |
| Generating Functions and Basic Statistics | p. 247 |
| Generating Functions for Recursive Trees | p. 248 |
| Generating Functions for Binary Search Trees | p. 249 |
| Generating Functions for Plane Oriented Recursive Trees | p. 251 |
| The Degree Distribution of Recursive Trees | p. 253 |
| The Insertion Depth | p. 262 |
| The Profile of Recursive Trees | p. 265 |
| The Martingale Method | p. 266 |
| The Moment Method | p. 275 |
| The Contraction Method | p. 278 |
| The Height of Recursive Trees | p. 280 |
| Profile and Height of Binary Search Trees and Related Trees | p. 291 |
| The Profile of Binary Search Trees and Related Trees | p. 291 |
| The Height of Binary Search Trees and Related Trees | p. 300 |
| Tries and Digital Search Trees | p. 307 |
| The Profile of Tries | p. 308 |
| Generating Functions for the Profile | p. 308 |
| The Expected Profile of Tries | p. 311 |
| The Limiting Distribution of the Profile of Tries | p. 321 |
| The Height of Tries | p. 323 |
| Symmetric Tries | p. 324 |
| The Profile of Digital Search Trees | p. 325 |
| Generating Functions for the Profile | p. 325 |
| The Expected Profile of Digital Search Trees | p. 327 |
| Symmetric Digital Search Trees | p. 337 |
| Recursive Algorithms and the Contraction Method | p. 343 |
| The Number of Comparisons in Quicksort | p. 345 |
| The L2 Setting of the Contraction Method | p. 350 |
| A General Type of Recurrence | p. 350 |
| A General L2 Convergence Theorem | p. 352 |
| Applications of the L2 Setting | p. 357 |
| Limitations of the L2 Setting and Extensions | p. 361 |
| The Zolotarev Metric | p. 362 |
| Degenerate Limit Equations | p. 363 |
| Planar Graphs | p. 365 |
| Basic Notions | p. 366 |
| Counting Planar Graphs | p. 368 |
| Outerplanar Graphs | p. 368 |
| Series-Parallel Graphs | p. 376 |
| Quadrangulations and Planar Maps | p. 382 |
| Planar Graphs | p. 389 |
| Outerplanar Graphs | p. 396 |
| The Degree Distribution of Outerplanar Graphs | p. 396 |
| Vertices of Given Degree in Dissections | p. 400 |
| Vertices of Given Degree in 2-Connected Outerplanar Graphs | p. 404 |
| Vertices of Given Degree in Connected Outerplanar Graphs | p. 406 |
| Series-Parallel Graphs | p. 408 |
| The Degree Distribution of Series-Parallel Graphs | p. 408 |
| Vertices of Given Degree in Series-Parallel Networks | p. 415 |
| Vertices of Given Degree in 2-Connected Series-Parallel Graphs | p. 416 |
| Vertices of Given Degree in Connected Series-Parallel Graphs | p. 419 |
| All Planar Graphs | p. 420 |
| The Degree of a Rooted Vertex | p. 421 |
| Singular Expansions | p. 425 |
| Degree Distribution for Planar Graphs | p. 429 |
| Vertices of Degree 1 or 2 in Planar Graphs | p. 433 |
| Appendix | p. 439 |
| References | p. 445 |
| Index | p. 455 |
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