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This text consists of a series of exercises, plus some background information and explanations, starting with conics and ending with sheaves and cohomology. The first chapter on conics is appropriate for first-year college students (and many high school students). Chapter 2 leads the reader to an understanding of the basics of cubic curves, while Chapter 3 introduces higher degree curves. Both chapters are appropriate for people who have taken multivariable calculus and linear algebra. Chapters 4 and 5 introduce geometric objects of higher dimension than curves. Abstract algebra now plays a critical role, making a first course in abstract algebra necessary from this point on. The last chapter is on sheaves and cohomology, providing a hint of current work in algebraic geometry.

Geometry, Algebraic --- Géométrie algébrique --- Algebraic geometry --- Instructional exposition (textbooks, tutorial papers, etc.) --- Geometry --- Géométrie algébrique. --- Geometry, Algebraic. --- Algebraic geometry -- Instructional exposition (textbooks, tutorial papers, etc.)

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Group theory --- Kac-Moody algebras. --- Linear algebraic groups. --- Geometry, Algebraic. --- Kac-Moody, Algèbres de --- Groupes linéaires algébriques --- Géométrie algébrique --- 51 <082.1> --- Mathematics--Series --- Geometry Algebraic --- Linear algebraic groups --- Geometry Algebraic. --- Kac-Moody, Algèbres de --- Groupes linéaires algébriques --- Géométrie algébrique --- Geometry, Algebraic --- Kac-Moody algebras --- Algebraic groups, Linear --- Algebraic varieties --- Algebras, Kac-Moody --- Lie algebras --- Algebraic geometry --- Geometry