《离散与组合数学手册》出版的目的是为需要离散与组合数学信息的计算机科学家、工程师、数学家和学生、物理与社会科学家，以及相关的图书管理员提供一本全方位的参考书。本书的第一版是以准参考资料的形式，为在工作或学习中用到与本书主题相关知识的人准备的展现这类信息的第一手资料，第二版是对第一版的重大修订。它包括了大量的添加和更新，这些添加与更新在本书前言的后半部分进行了总结。本书的范围包括通常被认为是离散数学的一部分的许多领域，集中于被认为在计算机科学、工程和其他学科的应用中至关重要的信息。本书是一部大型的工具书。本书呈现材料的方式可以让读者快速、轻松地找到和使用关键信息。每章都包含一个词汇表，用来对该章节中最重要的术语提供简洁的定义。单独的主题包含在每章的各个部分和小节中，每个部分都是清晰可辨的：定义、事实和示例。

1. FOUNDATIONS
1.1 Propositional and Predicate Logic - Jerrold W. Grossman
1.2 Set Theory - Jerrold W. Grossman
1.3 Functions - Jerrold W. Grossman
1.4 Relations - John G. Michaels
1.5 Proof Techniques - Susanna S. Epp
1.6 Axiomatic Program Verification - David Riley
1.7 Logic-Based Computer Programming Paradigms - Mukesh Dalal
2. COUNTING METHODS
2.1 Summary of Counting Problems - John G. Michaels
2.2 Basic Counting Techniques - Jay Yellen
2.3 Permutations and Combinations - Edward W. Packel
2.4 Inclusion/Exclusion - Robert G. Rieper
2.5 Partitions - George E. Andrews and Andrew V. Sills
2.6 Burnside/Pólya Counting Formula - Alan C. Tucker
2.7 M?bius Inversion Counting - Edward A. Bender
2.8 Young Tableaux - Bruce E. Sagan
3. SEQUENCES
3.1 Special Sequences - Thomas A. Dowling and Douglas R. Shier
3.2 Generating Functions - Ralph P. Grimaldi
3.3 Recurrence Relations - Ralph P. Grimaldi
3.4 Finite Differences - Jay Yellen
3.5 Finite Sums and Summation - Victor S. Miller
3.6 Asymptotics of Sequences - Edward A. Bender and Juanjo Rué
3.7 Mechanical Summation Procedures - Kenneth H. Rosen
4. NUMBER THEORY
4.1 Basic Concepts - Kenneth H. Rosen
4.2 Greatest Common Divisors - Kenneth H. Rosen
4.3 Congruences - Kenneth H. Rosen
4.4 Prime Numbers - Jon F. Grantham and Carl Pomerance
4.5 Factorization - Jon F. Grantham and Carl Pomerance
4.6 Arithmetic Functions - Kenneth H. Rosen
4.7 Primitive Roots and Quadratic Residues - Kenneth H. Rosen
4.8 Diophantine Equations - Bart E. Goddard
4.9 Diophantine Approximation - Jeff Shalit
4.10 Algebraic Number Theory - Lawrence C. Washington
4.11 Elliptic Curves - Lawrence C. Washington
5. ALGEBRAIC STRUCTURES - John G. Michaels
5.1 Algebraic Models
5.2 Groups
5.3 Permutation Groups
5.4 Rings
5.5 Polynomial Rings
5.6 Fields
5.7 Lattices
5.8 Boolean Algebras
6. LINEAR ALGEBRA
6.1 Vector Spaces - Joel V. Brawley
6.2 Linear Transformations - Joel V. Brawley
6.3 Matrix Algebra - Peter R. Turner
6.4 Linear Systems - Barry Peyton and Esmond Ng
6.5 Eigenanalysis - R. B. Bapat
6.6 Combinatorial Matrix Theory - R. B. Bapat and Geir Dahl
6.7 Singular Value Decomposition - Carla D. Martin
7. DISCRETE PROBABILITY
7.1 Fundamental Concepts - Joseph R. Barr
7.2 Independence and Dependence - Joseph R. Barr
7.3 Random Variables - Joseph R. Barr
7.4 Discrete Probability Computations - Peter R. Turner
7.5 Random Walks - Patrick Jaillet
7.6 System Reliability - Douglas R. Shier
7.7 Discrete-Time Markov Chains - Vidyadhar G. Kulkarni
7.8 Hidden Markov Models — Narada Warakagoda
7.9 Queueing Theory - Vidyadhar G. Kulkarni
7.10 Simulation - Lawrence M. Leemis
7.11 The Probabilistic Method - Niranjan Balachandran
8. GRAPH THEORY
8.1 Introduction to Graphs - Lowell W. Beineke
8.2 Graph Models - Jonathan L. Gross
8.3 Directed Graphs - Stephen B. Maurer
8.4 Distance, Connectivity, Traversability, & Matchings - Edward R. Scheinerman and Michael D. Plummer
8.5 Graph Isomorphism and Reconstruction - Bennet Manvel, Adolfo Piperno and Josef Lauri
8.6 Graph Colorings, Labelings, & Related Parameters - Arthur T. White, Teresa W. Haynes, Michael A. Henning, Glenn Hurlbert, and Joseph A. Gallian
8.7 Planar Drawings - Jonathan L. Gross
8.8 Topological Graph Theory - Jonathan L. Gross
8.9 Enumerating Graphs - Paul K. Stockmeyer
8.10 Graph Families - Maria Chudnovsky, Michael Doob, Michael Krebs, Anthony Shaheen, Richard Hammack, Sandi Klavzar, and Wilfried Imrich
8.11 Analytic Graph Theory - Stefan A. Burr
8.12 Hypergraphs — András Gyárfás
9. TREES
9.1 Characterizations and Types of Trees - Lisa Carbone
9.2 Spanning Trees - Uri Peled
9.3 Enumerating Trees - Paul K. Stockmeyer
10. NETWORKS AND FLOWS
10.1 Minimum Spanning Tr