The book covers topics in the theory of algebraic transformation groups and algebraic varieties which are very much at the frontier of mathematical research.

Factoriality Of Certain Hypersurfaces Of P4 With Ordinary Double Points.- Boundedness For Low Codimensional Subvarieties.- Normality and Non Normality Of Certain Semigroups and Orbit Closures.- Deformation Rigidity Of the 20-dimensional F4-homogeneous Space Associated To a Short Root.- Severi-Brauer Varieties and Symmetric Powers.- Representation Theory and Projective Geometry.- Geometric Realization Of T-shaped Root Systems and Counterexamples To Hilbert's Fourteenth Problem.- Self-dual Projective Algebraic Varieties Associated With Symmetric Spaces.- The Role Of Exotic Affine Spaces In the Classification Of Homogeneous Affine Varieties.- Hermitian Characteristics Of Nilpotent Elements.- Determinants Of Projective Varieties and Their Degrees.