one version of analytic spaces over nonarchimedean fields.
The original articles are
Roland Huber, Continuous valuations, Math. Z., 212(3):455{477, 1993
Roland Huber, A generalization of formal schemes and rigid analytic varieties. Math. Z., 217(4):513{551, 1994.
Roland Huber,_ Etale cohomology of rigid analytic varieties and adic spaces_. Aspects of Mathematics, E30. Friedr. Vieweg & Sohn, Braunschweig, 1996.
Review with an eye towards perfectoid spaces is in
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