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In this paper we survey research on the essential dimension that was introduced by J. Buhler and Z. Reichstein. Informally speaking, the essential dimension of a class of algebraic objects is the minimal number of algebraically independent parameters one needs to define any object in the class. The notion of essential dimension, which is defined in elementary terms, has surprising connections to many areas of algebra, such as algebraic geometry, algebraic K-theory, Galois cohomology,doi:10.1090/bull/1564 fatcat:yyce3plsozfubfs6ijqe6u2ghy