Algebras with the Same (Algebraic) Geometry

Some basic notions of classical algebraic geometry can be defined on arbitrary varieties of algebras $\Theta$. For every algebra $H$ in $\Theta$, one can consider algebraic geometry in $\Theta$ over $H$. Correspondingly, algebras in $\Theta$ are considered with the emphasis on equations and geometry. We give examples of geometric properties of algebras in $\Theta$ and of geometric relations between them. The main problem considered in the paper is when different $H_1$ and $H_2$ have the same geometry.