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(Abridged version) Mayall II = G1 is one of the brightest globular clustersbelonging to M31, the Andromeda galaxy. Our observations with HST/WFPC2 providedata for the (I vs. V-I) and (V vs. V-I) color-magnitude diagrams. From modelfitting, we determine a rather high mean metallicity of [Fe/H] = --0.95 +-0.09, somewhat similar to 47 Tucanae. We find a larger spread in V-I than canbe explained by the measurement errors, and we attribute this to an intrinsicmetallicity dispersion amongst the stars of G1. So far, only omega Centauri,the giant Galactic globular cluster, has been known to exhibit such anintrinsic metallicity dispersion.  Three estimates of the total mass of this globular cluster can be obtained:King mass = 15 x 10^6 with M/Lv ~ 7.5, Virial mass = 7.3 x 10^6 with M/Lv ~3.6, and King-Michie mass range from 14 to 17 x 10^6. Although uncertain, allof these mass estimates make G1 more than twice as massive as omega Centauri.  Such large masses relate to the metallicity spread whose origin is stillunknown (either self-enrichment, an inhomogeneous proto-cluster cloud, orremaining core of a dwarf galaxy). When considering the positions of G1 in thedifferent diagrams defined by Kormendy (1985), G1 always appears on thesequence defined by globular clusters, and definitely away from the othersequences defined by elliptical galaxies, bulges, and dwarf spheroidalgalaxies. The same is true for omega Centauri and for the nucleus of the dwarfelliptical NGC 205. This does not prove that all (massive) globular clustersare the remnant cores of nucleated dwarf galaxies.Comment: 24 pages, 5 figures, accepted for publication in AJ (August 2001

Mayall II = G1 in M31: Giant Globular Cluster or Core of a Dwarf Elliptical Galaxy?