The Framework for Unified and Robust data Analysis with JAX (Furax) is an open-source Python framework for modeling data acquisition systems and solving inverse problems in astrophysics and cosmology. Built on JAX, Furax provides composable building blocks in the form of general-purpose and domain-specific linear operators, along with preconditioners and solvers for their numerical inversion. Domain-specific tools are provided for astrophysical and cosmic microwave background (CMB) data analysis$-$including map-making, instrument modeling, and astrophysical component separation$-$with a modular architecture designed to extend to other fields.