- Ch. 1Elements and SetsA set is given by a property; deciding membership often means rephrasing it.
- Ch. 2Operations on SetsThree sets cut U into 8 regions; equal sets shade exactly the same regions.
- Ch. 3Counting the Elements of a Finite SetToo hard to count? Count 0-1 strings, or split by the last element.
- Ch. 4Partitions of a SetCut a set into disjoint pieces; restrict the cuts and “impossible” is a theorem.
- Ch. 5Families of SubsetsHow big can a family of subsets obeying a rule be? Pair them up or chain them.
- Ch. 6Properties of SetsA rule and a few elements force much into a set; an invariant shows the limit.
- Ch. 7The Principle of ClassificationSplit a messy whole into disjoint classes; the art is choosing the criterion.
- Ch. 8The Extremal PrincipleA finite set of numbers has a largest and a smallest. Grab the extreme one.
- Ch. 9Inclusion–ExclusionAdd, subtract the overlaps, add back… until every element is counted once.