Introduction; 1. System of coordinates; 2. The linear complex; 3. Synthesis of the linear complex; 4. Systems of linear complexes; 5. Ruled cubic and quartic surfaces; 6. The quadratic complex; 7. Special varieties of the quadratic complex; 8. The cosingular complexes; 9. Polar lines, points, and planes; 10. Representation of a complex by points of space; 11. The general equation of the second degree; 12. Connexion of line-geometry with sphere-geometry; 13. Connexion of line-geometry with hypergeometry; 14. Congruence of lines; 15. Congruences of the second order without singular curves; 16. The congruence of the second order and second class; 17. The general complex; 18. Differential equations connected with the line complex; Miscellaneous results and exercises; Index.