CH-Quasigroups and Moufang Loops. Classes of Points on Cubic Hypersurfaces. Two-Dimensional Birational Geometry. The Twenty-Seven Lines. Minimal Cubic Surfaces. The Brauer-Grothendieck Group.
Appendix: Algebraic Varieties Close to the Rational Ones. Algebra, Geometry, Arithmetic. Galois Cohomology, Picard Groups and Birational Geometry. The Hasse Principle and Descent on Rational Varieties. Geometry of Rational Surfaces. Complements. The Luroth Problem and the Zariski Problem in Dimension 3. Rational Points and Equivalence Relations. Cubic Surfaces and Commutative Loops (CML). References. Subject Index.