Notation
1. Introduction and Sperner's theorem
1.1 A simple intersection result
1.2 Sperner's theorem
1.3 A theorem of Bollobás
Exercises 1
2. Normalized matchings and rank numbers
2.1 Sperner's proof
2.2 Systems of distinct representatives
2.3 LYM inequalities and the normalized matching property
2.4 Rank numbers: some examples
Exercises 2
3. Symmetric chains
3.1 Symmetric chain decompositions
3.2 Dilworth's theorem
3.3 Symmetric chains for sets
3.4 Applications
3.5 Nested Chains
3.6 Posets with symmetric chain decompositions
Exercises 3
4. Rank numbers for multisets
4.1 Unimodality and log concavity
4.2 The normalized matching property
4.3 The largest size of a rank number
Exercises 4
5. Intersecting systems and the Erdös-Ko-Rado theorem
5.1 The EKR theorem
5.2 Generalizations of EKR
5.3 Intersecting antichains with large members
5.4 A probability application of EKR
5.5 Theorems of Milner and Katona
5.6 Some results related to the EKR theorem
Exercises 5
6. Ideals and a lemma of Kleitman
6.1 Kleitman's lemma
6.2 The Ahlswede-Daykin inequality
6.3 Applications of the FKG inequality to probability theory
6.4 Chvátal's conjecture
Exercises 6
7. The Kruskal-Katona theorem
7.1 Order relations on subsets
7.2 The l-binomial representation of a number
7.3 The Kruskal-Katona theorem
7.4 Some easy consequences of Kruskal-Katona
7.5 Compression
Exercises 7
8. Antichains
8.1 Squashed antichains
8.2 Using squashed antichains
8.3 Parameters of intersecting antichains
Exercises 8
9. The generalized Macaulay theorem for multisets
9.1 The theorem of Clements and Lindström
9.2 Some corollaries
9.3 A minimization problem in coding theory
9.4 Uniqueness of a maximum-sized antichains in multisets
Exercises 9
10. Theorems for multisets
10.1 Intersecting families
10.2 Antichains in multisets
10.3 Intersecting antichains
Exercises 10
11. The Littlewood-Offord problem
11.1 Early results
11.2 M-part Sperner theorems
11.3 Littlewood-Offord results
Exercises 11
12. Miscellaneous methods
12.1 The duality theorem of linear programming
12.2 Graph-theoretic methods
12.3 Using network flow
Exercises 12
13. Lattices of antichains and saturated chain partitions
13.1 Antichains
13.2 Maximum-sized antichains
13.3 Saturated chain partitions
13.4 The lattice of k-unions
Exercises 13
Hints and solutions; References; Index

Coherent treatment provides comprehensive view of basic methods and results of the combinatorial study of finite set systems. The Clements-Lindstrom extension of the Kruskal-Katona theorem to multisets is explored, as is the Greene-Kleitman result concerning k-saturated chain partitions of general partially ordered sets. Connections with Dilworth's theorem, the marriage problem, and probability are also discussed. Each chapter ends with a helpful series of exercises and outline solutions appear at the end. "An excellent text for a topics course in discrete mathematics." ? Bulletin of the American Mathematical Society.