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This course will be on functional analysis (applied to number theory) and Connes-Meyer's spectral interpretation of zeroes of Hecke L functions. Topics will include : adeles, ideles, bornologies, spectral theory, condensed/liquid modules à la Scholze-Clausen, Pontryagin duality and almost-periodic functions, Tate's thesis, Connes-Meyer's spectral interpretation. Relations with category theory, quantum mechanics, Bost-Connes systems and non-commutative geometry will be evoked. This course will be designed to be appealing for students from analysis or from algebra.