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

These are the proceedings of the conference Interesting Algebraic Varieties Arising in Algebraic Transformation Groups Theory that was held at The Erwin Schr] odinger International Institute for Mathematical Physics, Vienna, Austria, from October 22 through October 26, 2001. Theconferencewasmadepossiblethroughinterestand?nancialandor- nizational support of The Erwin Schrodinger ] International Institute for - thematicalPhysics, Vienna, Austria. Onbehalf ofall participantsI thank this institution and especially P. W. Michor, one of its Directors, for this interest and support. It is an empirical fact that many interesting and important algebraic va- eties are intimately related to algebraic transformation groups. To name only some, the examples are a?ne and projective spaces; quadrics; grassman- ans, ?ag and, more generally, spherical (in particular toric) varieties; Sc- bert varieties; nilpotent varieties; determinantal varieties, Severi, Scorza and, more generally, highest vector (HV-) varieties; group varieties; generic tori in algebraic groups; commuting varieties; categorical quotients of Geometric Invariant Theory and the related moduli varieties of curves, vector bundles, abelianvarietiesetc.;simple singularitiesrealizedasthatofthe corresponding categorical quotients and nilpotent orbit closures. The idea of the conference was to trace the new evidences of this relation. Forvariousreasonsseveraltalksgivenduringtheconferencedonotappear intheseproceedings.Belowacompletelistingofalltalksgivenispresentedfor theinformationabouttheconference.Thetalkswhichdoappeararegenerally expanded and/or modi?ed versions of those given during the conference. November 21, 2003 Vladimir L. Popov List of Talks Given at the Conference Interesting Algebraic Varieties Arising in Algebraic Transformation Groups Theory, ESI, Vienna, Austria, October 22 26, 2001 Monday, October 22, 2001 10.30 12.00 DavidJ.Saltman (University of Texas at Austin, Austin, USA), Invariants of Symplectic and Orthogonal Groups of Degree 8."