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http://mathworld.wolfram.com/AlgebraicGeometry.html
Algebraic geometry is the study of geometries that come from algebra, in particular, from rings. In classical algebraic geometry, the algebra is the ring of polynomials, and the geometry is the set of zeros of polynomials, called an algebraic variety.

http://www.math.purdue.edu/~dvb/algeom.html
Article by Donu Arapura giving an overview to the subject of algebraic geometry.