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Based on the distinction between the covariant and contravariant metrictensor components in the framework of the affine geometry approach and also onthe choice of the contravariant components, it was shown that a wide variety ofthird, fourth, fifth, sixth, seventh - degree algebraic equations exists ingravity theory. This fact, together with the derivation of the algebraicequations for a generally defined contravariant tensor components in thispaper, are important in view of finding new solutions of the Einstein'sequations, if they are treated as algebraic ones. Some important properties ofthe introduced in hep-th/0107231 more general connection have been also proved- it possesses affine transformation properties and it is an equiaffine one.Basic and important knowledge about the affine geometry approach and aboutgravitational theories with covariant and contravariant connections and metricsis also given with the purpose of demonstrating when and how these theories canbe related to the proposed algebraic approach and to the existing theory ofgravity and relativistic hydrodynamics.

Elliptic Curves and Algebraic Geometry Approach in Gravity Theory I.The General Approach