The first part, covering three chapters and roughly the first quarter of the book, concerns the symbolic method in combinatorics, in which classes of combinatorial objects are associated with formulas that describe their structures, and then those formulas are reinterpreted to produce the generating functions or exponential generating functions of the classes,[1][2] in some cases using tools such as the Lagrange inversion theorem as part of the reinterpretation process.

[1] After an introductory chapter and a chapter giving examples of the possible behaviors of rational functions and meromorphic functions, the remaining chapters of this part discuss the way the singularities of a function can be used to analyze the asymptotic behavior of its power series, apply this method to a large number of combinatorial examples, and study the saddle-point method of contour integration for handling some trickier examples.

[4] Nevertheless, it can be used as the textbook for an upper-level undergraduate elective,[5] graduate course,[4] or seminar,[3] although reviewer Miklós Bóna writes that some selection is needed, as it "has enough material for three or more semesters".

The award citation called the book "an authoritative and highly accessible compendium of its subject, which demonstrates the deep interface between combinatorial mathematics and classical analysis".

[5] Although the application of analytic methods in combinatorics goes back at least to the work of G. H. Hardy and Srinivasa Ramanujan on the partition function,[1] the citation also quoted a review by Robin Pemantle stating that "This is one of those books that marks the emergence of a subfield," the subfield of analytic combinatorics.