"giGa": The Billion Galaxy HI Survey - Tracing galaxy assembly from reionization to the present

In this paper, we review the Billion Galaxy Survey that will be carried out at radio - optical wavelengths to micro - nanoJansky levels with the telescopes of the next decades. These are the Low-Frequency Array, the Square Kilometer Array and the Large Synoptic Survey Telescope as survey telescopes, and the Thirty Meter class Telescopes for high spectral resolution plus AO, and the James Webb Space Telescope (JWST) for high spatial resolution near - mid-IR follow-up. With these facilities, we will be addressing fundamental questions like how galaxies assemble with super-massive black-holes inside from the epoch of First Light until the present, how these objects started and finished the reionization of the universe, and how the processes of star-formation, stellar evolution, and metal enrichment of the IGM proceeded over cosmic time. We also summarize the high-resolution science that has been done thus far on high redshift galaxies with the Hubble Space Telescope (HST). Faint galaxies have steadily decreasing sizes at fainter fluxes and higher redshifts, reflecting the hierarchical formation of galaxies over cosmic time. HST has imaged this process in great structural detail to z≲6. We show that ultradeep radio - optical surveys may slowly approach the natural confusion limit, where objects start to unavoidably overlap because of their own sizes, which only SKA can remedy with HI redshifts for individual sub-clumps. Finally, we summarize how the 6.5 meter James Webb Space Telescope (JWST) will measure first light, reionization, and galaxy assembly in the near - mid-IR.