1. Geometric matrix models i; 2. Geometric matrix models ii; 3. From matrices to rank 3 oriented matroids; 4. Oriented matroids of arbitrary rank; 5. From oriented matroids to face lattices; 6. From face lattices to oriented matroids i; 7. From face lattices to oriented matroids ii; 8. From oriented matroids to matrices; 9. Computational synthetic geometry; 10. Some oriented matroid applications; 11. Some inttrinsic oriented matroid problems; Bibliography; Index.