| Preface | p. ix |
| An Invitation to Analytic Combinatorics | p. 1 |
| Symbolic Methods | p. 13 |
| Combinatorial Structures and Ordinary Generating Functions | p. 15 |
| Symbolic enumeration Methods | p. 16 |
| Admissible constructions and specifications | p. 24 |
| Integer compositions and partitions | p. 39 |
| Words and regular languages | p. 49 |
| Tree structures | p. 64 |
| Additional constructions | p. 83 |
| Perspective | p. 92 |
| Labelled Structures and Exponential Generating Functions | p. 95 |
| Labelled classes | p. 96 |
| Admissible labelled constructions | p. 100 |
| Surjections, set partitions, and words | p. 106 |
| Alignments, permutations, and related structures | p. 119 |
| Labelled trees, mapping, and graphs | p. 125 |
| Additional constructions | p. 136 |
| Perspective | p. 147 |
| Combinatorial Parameters and Multivariate Generating Functions | p. 151 |
| An introduction to bivariate generating functions (BGFs) | p. 152 |
| Bivariate generating functions and probability distributions | p. 156 |
| Inherited parameters and ordinary MGFs | p. 163 |
| Inherited parameters and exponential MGFs | p. 174 |
| Recursive parameters | p. 181 |
| Complete generating functions and discrete models | p. 186 |
| Additional constructions | p. 198 |
| Extremal parameters | p. 214 |
| Perspective | p. 218 |
| Complex Asymptotics | p. 221 |
| Complex Analysis, Rational and Meromorphic Asymptotics | p. 223 |
| Generating functions as analytic objects | p. 225 |
| Analytic functions and meromorphic functions | p. 229 |
| Singularities and exponential growth of coefficients | p. 238 |
| Closure properties and computable bounds | p. 249 |
| Rational and meromorphic functions | p. 255 |
| Localization of singularities | p. 263 |
| Singularities and functional equations | p. 275 |
| Perspective | p. 286 |
| Applications Of Rational and Meromorphic Asymptotics | p. 289 |
| A roadmap to rational and meromorphic asymptotics | p. 290 |
| The supercritical sequence schema | p. 293 |
| Regular specifications and languages | p. 300 |
| Nested sequences, lattice paths, and continued fractions | p. 318 |
| Paths in graphs and automata | p. 336 |
| Transfer matrix models | p. 356 |
| Perspective | p. 373 |
| Singularity Analysis Of Generating Functions | p. 375 |
| A glimpse of basic singularity analysis theory | p. 376 |
| Coefficient asymptotics for the standard scale | p. 380 |
| Transfers | p. 389 |
| The process of singularity analysis | p. 392 |
| Multiple singularities | p. 398 |
| Intermezzo: functions amenable to singularity analysis | p. 401 |
| Inverse functions | p. 402 |
| Polylogarithms | p. 408 |
| Functional composition | p. 411 |
| Closure properties | p. 418 |
| Tauberian theory and Darboux's method | p. 433 |
| Perspective | p. 437 |
| Applications of Singularity Analysis | p. 439 |
| A roadmap to singularity analysis asymptotics | p. 441 |
| Sets and the exp-log schema | p. 445 |
| Simple varieties of trees and inverse functions | p. 452 |
| Tree-like structures and implicit functions | p. 467 |
| Unlabelled non-plane trees and Pólya operators | p. 475 |
| Irreducible context-free structures | p. 482 |
| The general analysis of algebraic functions | p. 493 |
| Combinatorial applications of algebraic functions | p. 506 |
| Ordinary differential equations and systems | p. 518 |
| Singularity analysis and probability distributions | p. 532 |
| Perspective | p. 538 |
| Saddle-Point Asymptotics | p. 541 |
| Landscapes of analytic functions and saddle-points | p. 543 |
| Saddle-point bounds | p. 546 |
| Overview of the saddle-point method | p. 551 |
| Three combinatorial examples | p. 558 |
| Admissibility | p. 564 |
| Integer partitions | p. 574 |
| Saddle-points and linear differential equations | p. 581 |
| Large powers | p. 585 |
| Saddle-points and probability distributions | p. 594 |
| Multiple saddle-points | p. 600 |
| Perspective | p. 606 |
| Random Structures | p. 609 |
| Multivariate Asymptotics and Limit Laws | p. 611 |
| Limit laws and combinatorial structures | p. 613 |
| Discrete limit laws | p. 620 |
| Combinatorial instances of discrete laws | p. 628 |
| Continuous limit laws | p. 638 |
| Quasi-powers and Guassian limit laws | p. 644 |
| Perturbation of meromorphic asymptotics | p. 650 |
| Pertubation of singularity analysis asymptotics | p. 666 |
| Perturbation of saddle-point asymptotics | p. 690 |
| Local limit laws | p. 694 |
| Large deviations | p. 699 |
| Non-Gaussian continuous limits | p. 703 |
| Multivariate limit laws | p. 715 |
| Perspective | p. 716 |
| Appendices | p. 719 |
| Auxiliary Elementary Notions | p. 721 |
| Arithmetical functions | p. 721 |
| Asymptotic notations | p. 721 |
| Combinatorial probability | p. 722 |
| Cycle construction | p. 729 |
| Formal power series | p. 730 |
| Lagrange inversion | p. 732 |
| Regular languages | p. 733 |
| Stirling numbers. | p. 735 |
| Tree Concepts | p. 737 |
| Basic Complex Analysis | p. 739 |
| Algebraic elimination | p. 739 |
| Equivalent definitions of analyticity | p. 741 |
| Gamma function | p. 743 |
| Holonomic functions | p. 748 |
| Implicit Function Theorem | p. 753 |
| Laplace's method | p. 755 |
| Mellin transforms | p. 762 |
| Several complex variables | p. 767 |
| Concepts Of Probability Theory | p. 769 |
| Probability spaces and measure | p. 769 |
| Random variables | p. 771 |
| Transforms of distributions | p. 772 |
| Special distributions | p. 774 |
| Convergence in law | p. 776 |
| Bibliography | p. 779 |
| Index | p. 801 |
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