1. Introduction 2. Terminology 3. Commutativity and the center 4. JW-algebras 5. Quadratic ideals 6. Annihilators 7. Type I 8. Some algebraic facts 9. Position $p'$ 10. Relations with perspectivity 11. Equivalence and central covers 12. Generalized comparability 13. Modularity and finiteness 14. The type decomposition 15. Some structure theory 16. Dimension functions 17. Dimension lattice structure 18. The trace 19. A new kind of factor 20. Concluding remarks