Algebraic transformation groups and algebraic varieties : proceedings of the Conference Interesting Algebraic Varieties Arising in Algebraic Transformation Group Theory held at the Erwin Schrödinger Institute Vienna October 22 26 2001 The book covers topics in the theory of algebraic transformation groups and algebraic varieties which are very much at the frontier of mathematical research. The contributors are all internationally well known specialists and hence the book will have great appeal to researchers and graduate students in mathematics and mathematical physics. TOC:1. Ciliberto Di Gennaro: Factoriality of Certain Hypersurfaces of P4 with Ordinary Double Points. 2. Ciliberto Di Gennaro: Boundness for Low Codimensional Subvarieties. 3. De Concini: Normality and Non Normality of Certain Semigroups and Orbit Closures. 4. Landsberg Manivel: Representation Theory and Projective Geometry. 5. Hwang Mok: Deformation Rigidity of the 20 Dimensional F_4 Homogeneous Space Associated to a Short Root. 6. Mukai: Geometric Realization of T Shaped Root Systems and Counterexamples to Hilberts Fourteenth Problem. 7. Krashen Saltman: Severi Brauer Varieties and Symmetric Powers. 8. Popov Tevelev: Self Dual Algebraic Varieties and Nilpotent Orbits in Symmetric Pairs. 9. Snow: The Role of Exotic Affine Spaces in the Classification of Homogeneous Affine Varieties. 10. Tevelev: Hermitian Characteristics of Nilpotent Elements. 11. Zak: Determinants of Projective Varieties and their Degrees