Strict analytic geometry is the study of analytic spaces over Banach rings with building blocs given by strict rational domains (defined, for example, by relations of the form $\{x,\;|f(x)|\leq |g(x)|\neq 0\}$) in polydiscs of radius one.

In the $p$-adic setting, strict analytic geometry is usually called rigid analytic geometry. In the archimedean setting (i.e., over $\C$), strict analytic geometry is essentially equivalent to usual analytic geometry.