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ABRIDGED) We revise the formation of Galactic GCs by adding the detailedchemical composition of their different stellar generations (from 1200 giantsin 19 GCs) to their global parameters. We propose to identify as GCs thoseshowing the Na-O anticorrelation, and we classify the GCs according tokinematics and location in the Galaxy in disk/bulge, inner, and outer halo. Wefind that the LF of GCs is fairly independent of their population, suggestingthat it is imprinted by the formation mechanism, and only marginally affectedby the ensuing evolution. We show that a large fraction of the primordialpopulation should have been lost by the proto-GCs. The extremely low Alabundances found for the primordial population of massive GCs indicate a veryfast enrichment process before the formation of the primordial population. Wesuggest a scenario for the formation of GCs including at least 3 main phases:i) the formation of a precursor population (likely due to the interaction ofcosmological structures similar to those leading to dwarf spheroidals, butresiding at smaller Rgc, with the early Galaxy or with other structures), ii)which triggers a large episode of star formation (the primordial population),and iii) the formation of the current GC, mainly within a cooling flow formedby the slow winds of a fraction of the primordial population. The precursorpopulation is very effective in raising the metal content in massive and/ormetal poor (mainly halo) clusters, while its role is minor in small and/ormetal rich (mainly disk) ones. Finally, we use PCA and multivariate relationsto study the phase of metal-enrichment from 1st to 2nd generation. Most of thechemical signatures of GCs may be ascribed to a few parameters, the mostimportant being [Fe/H], mass, and age of the cluster, with the location withinthe Galaxy also playing some role.

Properties of stellar generations in Globular Clusters and relations with global parameters