I. Introduction.- 1. Set Systems and Languages.- 2. Graphs, Partially Ordered Sets and Lattices.- II. Abstract Linear Dependence - Matroids.- 1. Matroid Axiomatizations.- 2. Matroids and Optimization.- 3. Operations on Matroids.- 4. Submodular Functions and Polymatroids.- III. Abstract Convexity - Antimatroids.- 1. Convex Geometries and Shelling Processes.- 2. Examples of Antimatroids.- 3. Circuits and Paths.- 4. Helly's Theorem and Relatives.- 5...