If you only read one chapter, make it Chapter 4: "Generating Functions." Riordan shows that the ordinary generating function $A(x) = \sum_n \ge 0 a_n x^n$ is not just a formal power series—it is a calculus .

John Riordan's An Introduction to Combinatorial Analysis (1958) is a landmark text that helped transform combinatorics from a collection of isolated puzzles into a unified mathematical discipline. Riordan defines the subject simply as determining "the number of ways there are of doing some well-defined operation". www.amazon.com Core Concepts and Structure

This is perhaps the "exclusive" heart of the book. Riordan explores the theory of rook polynomials and permutations that must avoid certain patterns—a precursor to modern pattern-avoidance theory.