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We perform high-resolution cosmological hydrodynamic simulations to study theformation of the first galaxies that reach the masses of$10^{8-9}~h^{-1}~M_\odot$ at $z=9$. The resolution of the simulations is highenough to resolve minihaloes and allow us to successfully pursue the formationof multiple Population (Pop) III stars, their supernova (SN) explosions,resultant metal-enrichment of the inter-galactic medium (IGM) in the course ofthe build-up of the system. Metals are ejected into the IGM by multiple Pop IIISNe, but some of the metal-enriched gas falls back onto the halo after $\gtrsim100~\rm Myr$. The star formation history of the first galaxy dependssensitively on the initial mass function (IMF) of Pop III stars. The dominantstellar population transits from Pop III to Pop II at $z\sim 12-15$ in the caseof power-law Pop III IMF, ${\rm d}n/{\rm d}M \propto M^{-2.35}$ with the massrange $10-500~M_\odot$. At $z\lesssim 12$, stars are stably formed in the firstgalaxies with a star formation rate of $\sim 10^{-3}$-$10^{-1}~M_\odot/{\rmyr}$. In contrast, for the case with a flat IMF, gas-deprived first galaxiesform due to frequent Pop III pair-instability SNe, resulting in the suppressionof subsequent Pop II star formation. In addition, we calculate UV continuum,Ly$\alpha$- and H$\alpha$-line fluxes from the first galaxies. We show that theJames Webb Space Telescope will be able to detect both UV continuum, Ly$\alpha$and H$\alpha$ line emission from first galaxies with halo mass $\gtrsim10^{9}~M_\odot$ at $z \gtrsim 10$.

Formation of the first galaxies in the aftermath of the first supernovae