I. Basic Methods
Chapter 1: Seven Is More Than Six. The Pigeon-Hole Principle
Chapter 2: One Step at a Time. The Method of Mathematical Induction

II. Enumerative Combinatorics
Chapter 3: There Are A Lot Of Them. Elementary Counting Problems
Chapter 4: No Matter How You Slice It. The Binomial Theorem and Related Identities
Chapter 5: Divide and Conquer. Partitions
Chapter 6: Not So Vicious Cycles. Cycles in Permutations
Chapter 7: You Shall Not Overcount. The Sieve
Chapter 8: A Function Is Worth Many Numbers. Generating Functions

III. Graph Theory
Chapter 9: Dots and Lines. The Origins of Graph Theory
Chapter 10: Staying Connected. Trees
Chapter 11: Finding A Good Match. Coloring and Matching
Chapter 12: Do Not Cross. Planar Graphs

IV. Horizons
Chapter 13: Does It Clique? Ramsey Theory
Chapter 14: So Hard To Avoid. Subsequence Conditions on Permutations
Chapter 15: Who Knows What It Looks Like, But It Exists. The Probabilistic Method
Chapter 16: At Least Some Order. Partial Orders and Latticesc
Chapter 17: As Evenly As Possible. Block Designs and Error Correcting Codes
Chapter 18: Are They Really Different? Counting Unlabeled Structures
Chapter 19: The Sooner The Better. Combinatorial Algorithms
Chapter 20: Does Many Mean More Than One? Computational Complexity

This is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course.

Just as with the first three editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs. ---summary provided by publisher