CONTENTS Introduction 1 1. Elementar y propertie s o f polynomia l ring s 2 2. Affin e space s and projective space s 5 3. Rule d surface s an d rationa l surface s 1 1 4. Automorphis m group s o f polynomia l ring s 1 5 5. Cremon a group s 1 7 6. Grou p action s o n affin e ring s 2 1 7. Complet e reducibilit y o f rationa l representation s 2 3 8. Ring s of invariants 2 5 9. Som e remark s o n orbit s 3 0 References 3 2
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