Algebraic geometry is a branch of mathematics, which combines abstract algebra, especially commutative algebra, with geometry. It can be regarded as a study of the solution set of algebraic equations. Algebraic geometry takes algebraic clusters as the research object. Algebraic cluster is the locus of points determined by one or more algebraic equations of spatial coordinates. For example, algebraic clusters in three-dimensional space are algebraic curves and algebraic surfaces. Algebraic geometry studies the geometric properties of general algebraic curves and surfaces.

Algebraic geometry has extensive relations with many branches of mathematics, such as complex analysis, number theory, analytic geometry, differential geometry, commutative algebra, algebraic groups, topology and so on. The development of algebraic geometry and these disciplines play a mutually promoting role.