Star formation is a crucial process throughout astrophysics that underpins the evolution of galaxies, stellar populations and the conditions for the birth of planets around young stars. We propose to carry out several suites of numerical simulations that investigate star formation across a wide range of scales. First, we will study large-scale star formation in galaxies (spanning domains of ~millions of light years), with a focus on the early formation and growth of galaxies, including their supermassive black holes (SMBHs). Such studies are particularly relevant to interpret latest observations from JWST. Second, we will examine intermediate-scale star formation as found in giant molecular clouds (GMCs) (spanning domains of ~hundreds of light years). Most stars in our Galaxy, the Milky Way, are born in GMCs and these objects can be resolved in great detail by radio and infrared telescopes, including ALMA and JWST. Here, our focus is to model the chemical evolution in collapsing, magnetized clouds, just before they form stars. This is essential to understand the physical evolution, since chemistry affects the ionization degree and thus the coupling of gas to magnetic fields, which are known to regulate the collapse. The chemistry also sets the abundances of various molecules that act as important diagnostic tracers of the clouds that can be observed by ALMA and JWST. Third, we will investigate star formation on very small scales, carrying out very high resolution simulations of the accretion of gas to stellar surfaces (spanning domains of ~light hours, i.e., Solar-System scales). For this we will resolve inner regions of the disk of gas that mediates accretion and growth of a star, studying cases relevant to low-mass stars, like our Sun, and high-mass stars, i.e., > 8Msun, that eventually explode as supernovae. This accretion disk also launches powerful outflows, i.e., “disk winds”, that are important for regulating the efficiency of star formation. The disk is also the location for planet formation, so modeling its structure and evolution are necessary steps for understanding the birth of planets. The simulations to be performed in the above sub-projects will utilize grid-based simulation codes (i.e., RAMSES, Enzo, PLUTO), having a common theme of following magnetohydrodynamics (MHD) and detailed treatments of thermodynamics, i.e., heating and cooling processes. Our group has extensive experience of using and developing these codes, and all three sub-projects have significant prior background work either already published or in an advanced state of preparation.