I would like to add the nine volumes of the "Treatise on Analysis" of Jean Dieudonné (in French, "Éléments d'Analyse") which is quite thorough with beautiful exercises (unfortunately some of them contain errors or wrong hints) and give a broad view of contemporary aspects of Analysis, still useful nowadays especially the ninth & last volume (they were published in the 70s and 80s I think). Written with a flavor of Bourbaki, it gives the right level of generality (not too much, usually using only locally compact metrizable groups) and the numerous exercises really help to master maim results and methods of proof.