doi:10.4171/DM/1006engElduque, AlbertoKochetov, MikhailAlmost fine gradings on algebras and classification of gradings up to isomorphismART-2025-144519We consider the problem of classifying gradings by groups on a finite-dimensional algebra A (with any number of multilinear operations) over an algebraically closed field. We introduce a class of gradings, which we call almost fine, such that every G-grading on A is obtained from an almost fine grading on A in an essentially unique way, which is not the case with fine gradings. For abelian G, we give a method of obtaining all almost fine gradings if fine gradings are known. We apply these ideas to the case of semisimple Lie algebras in characteristic 0: to any abelian group grading with nonzero identity component, we attach a (possibly nonreduced) root system Φ and, in the simple case, construct an adapted Φ-grading.2025http://zaguan.unizar.es/record/16188210.4171/DM/1006http://zaguan.unizar.es/record/161882oai:zaguan.unizar.es:161882info:eu-repo/grantAgreement/ES/DGA/E22-23Rinfo:eu-repo/grantAgreement/EUR/ISCII-ERDF/A way to make Europeinfo:eu-repo/grantAgreement/ES/MCINN/PID2021-123461NB-C21Documenta Mathematica 30, 4 (2025), 887-908byhttps://creativecommons.org/licenses/by/4.0/deed.esinfo:eu-repo/semantics/openAccess