We present the science case and observations plan of the MeerKAT Fornax Survey, an HI and radio continuum survey of the Fornax galaxy cluster to be carried out with the SKA precursor MeerKAT. Fornax is the second most massive cluster within 20 Mpc and the largest nearby cluster in the southern hemisphere. Its low X-ray luminosity makes it representative of the environment where most galaxies live and where substantial galaxy evolution takes place. Fornaxs ongoing growth makes it an excellent laboratory for studying the assembly of clusters, the physics of gas accretion and stripping in galaxies falling in the cluster, and the connection between these processes and the neutral medium in the cosmic web. We will observe a region of 12 deg$^2$ reaching a projected distance of 1.5 Mpc from the cluster centre. This will cover a wide range of environment density out to the outskirts of the cluster, where gas-rich in-falling groups are found. We will: study the HI morphology of resolved galaxies down to a column density of a few times 1e+19 cm$^{-2}$ at a resolution of 1 kpc; measure the slope of the HI mass function down to M(HI) 5e+5 M(sun); and attempt to detect HI in the cosmic web reaching a column density of 1e+18 cm$^{-2}$ at a resolution of 10 kpc.
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