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Magnetic materials with kagome crystal structure exhibit rich physics, such as frustrated magnetism, skyrmion formation, topological flat bands, and Dirac/Weyl points. Until recently, most studies on kagome magnets have been performed on bulk crystals or polycrystalline films. Here, we report the atomic layer molecular beam epitaxy synthesis of high-quality thin films of topological kagome magnet Fe3Sn2. The structural and magnetic characterization of Fe3Sn2 on epitaxial Pt(111) identifies highly ordered films with c-plane orientation and an in-plane magnetic easy axis. Studies on the local magnetic structure by anomalous Nernst effect imaging reveal in-plane oriented micrometer size domains. Superlattice structures consisting of Fe3Sn2 and Fe3Sn are also synthesized by atomic layer molecular beam epitaxy, demonstrating the ability to modulate the sample structure at the atomic level. The realization of high-quality films by atomic layer molecular beam epitaxy opens the door to explore the rich physics of this system and investigate novel spintronic phenomena by interfacing Fe3Sn2 with other materials.