1. Matrix Problems.- 2. Algebras, Modules and Categories.- 3. Radical, Decomposition, Aggregates.- 4. Finitely Spaced Modules.- 5. Finitely Represented Posets.- 6. Roots.- 7. Representations of Quivers.- 8. Spectroids, Quivers, Coherence.- 9. Almost Split Sequences.- 10. Postprojective Components.- 11. Representations of Tame Quivers.- 12. Derivation and Tilting (by B. Keller).- 13. Multiplicative Bases.- 14. Finitely Represented Algebras.- List of Symbols.