Introduction to the Theory of Matroids

I. Equivalent Axiomatic Definitions and Elementary Properties of Matroids -- §1.1. The first rank-axiomatic definition of a matroid -- §1.2. The independence-axiomatic definition of a matroid -- §1.3. The second rank-axiomatic definition of a matroid -- §1.4. The circuit-axiomatic definition of a matroid -- §1.5. The basis-axiomatic definition of a matroid -- II. Further Properties of Matroids -- §2.1. The span mapping -- §2.2. The span-axiomatic definition of a matroid -- §2.3. Hyperplanes and cocircuits -- §2.4. The dual matroid -- III. Examples -- §3.1. Linear algebraic examples -- §3.2. Binary matroids -- §3.3. Elementary definitions and results from graph theory -- §3.4. Graph-theoretic examples -- §3.5. Combinatorial examples -- IV. Matroids and the Greedy Algorithm -- §4.1. Matroids and the greedy algorithm -- V. Exchange Properties for Bases of Matroids -- §5.1. Symmetric point exchange -- §5.2. Bijective point replacement -- §5.3. More on minors of a matroid -- §5.4. Symmetric set exchange -- §5.5. Bijective set replacement -- §5.6. A further symmetric set exchange property.