Abstract
The building of universal algebraic geometry, or algebraic geometry over algebraic structures, has been under construction for a quarter of a century. In our review article we will talk about the history of the development of the theory of universal algebraic geometry, the problems that brought it to life, and those that arise in the process of building this theory, the state in which we find universal algebraic geometry today, and, most importantly, about those directions in which it continues its natural growth.
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