  ABRIDGED) We revise the formation of Galactic GCs by adding the detailed
chemical composition of their different stellar generations (from 1200 giants
in 19 GCs) to their global parameters. We propose to identify as GCs those
showing the Na-O anticorrelation, and we classify the GCs according to
kinematics and location in the Galaxy in disk/bulge, inner, and outer halo. We
find that the LF of GCs is fairly independent of their population, suggesting
that it is imprinted by the formation mechanism, and only marginally affected
by the ensuing evolution. We show that a large fraction of the primordial
population should have been lost by the proto-GCs. The extremely low Al
abundances found for the primordial population of massive GCs indicate a very
fast enrichment process before the formation of the primordial population. We
suggest 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 of
cosmological structures similar to those leading to dwarf spheroidals, but
residing 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 formed
by the slow winds of a fraction of the primordial population. The precursor
population is very effective in raising the metal content in massive and/or
metal poor (mainly halo) clusters, while its role is minor in small and/or
metal rich (mainly disk) ones. Finally, we use PCA and multivariate relations
to study the phase of metal-enrichment from 1st to 2nd generation. Most of the
chemical signatures of GCs may be ascribed to a few parameters, the most
important being [Fe/H], mass, and age of the cluster, with the location within
the Galaxy also playing some role.

Astrophysics of Galaxies