The new ALMA observatory has factors of 20 increase in both resolution and sensitivity. It is revolutionizing the study of high redshift galaxies and forming planetary systems. I will provide a brief introduction to its capabilities and then describe in detail two projects: 1) observations of 600 galaxies at z = 0.3 to 4 for which we measure the ISM gas contents and observations at 0.1 arcsec resolution of the local ULRIG galaxy Arp 220. In the first project, we analyze the evolution of ISM contents, star formation rates and efficiencies and galaxy accretion rates with cosmic time and galaxy properties for the first time. We also derive the overall cosmic evolution of gas in galaxies for comparison with existing data on the star formation rate density. In the second project, we resolve both nuclei of the late stage merging galaxies and find spectacular properties for the two galactic nuclei.