ALMA Cycle 2 observations of the long wavelength dust emission in 180 star-forming (SF) galaxies are used to investigate the evolution of ISM masses at z = 1 to 6.4. The ISM masses exhibit strong increases from z = 0 to $rm <z>$ = 1.15 and further to $rm <z>$ = 2.2 and 4.8, particularly amongst galaxies above the SF galaxy main sequence (MS). The galaxies with highest SFRs at $rm <z>$ = 2.2 and 4.8 have gas masses 100 times that of the Milky Way and gas mass fractions reaching 50 to 80%, i.e. gas masses 1 - 4$times$ their stellar masses. For the full sample of galaxies, we find a single, very simple SF law: $rm SFR propto M_{rm ISM}^{0.9}$, i.e. a `linear dependence on the ISM mass -- on and above the MS. Thus, the galaxies above the MS are converting their larger ISM masses into stars on a timescale similar to those on the MS. At z $> 1$, the entire population of star-forming galaxies has $sim$5 - 10$times$ shorter gas depletion times ($sim0.2$ Gyr) than galaxies at low redshift. These {bf shorter depletion times are due to a different, dominant mode of SF in the early universe} -- dynamically driven by compressive, high dispersion gas motions and/or galaxy interactions. The dispersive gas motions are a natural consequence of the extraordinarily high gas accretion rates which must occur to maintain the prodigious SF.
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