The Fe56(n,γ) thermal neutron capture cross section and the Fe57 level scheme populated by this reaction have been investigated in this work. Singles γ-ray spectra were measured with an isotopically enriched Fe56 target using the guided cold neutron beam at the Budapest Reactor, and γγ-coincidence data were measured with a natural Fe target at the LWR-15 research reactor in ŘeŽ, Czech Republic. A detailed level scheme consisting of 448 γ rays populating/depopulating 97 levels and the capture state in Fe57 has been constructed, and ≈99% of the total transition intensity has been placed. The transition probability of the 352-keV γ ray was determined to be Pγ(352)=11.90±0.07 per 100 neutron captures. The Fe57 level scheme is substantially revised from earlier work and ≈33 previously assigned levels could not be confirmed while a comparable number of new levels were added. The Fe57γ-ray cross sections were internally calibrated with respect to H1 and S32γ-ray cross section standards using iron(III) acetylacetonate (C15H21FeO6) and iron pyrite (FeS2) targets. The thermal neutron cross section for production of the 352-keV γ-ray cross section was determined to be σγ(352)=0.2849±0.015 b. The total Fe56(n,γ) thermal radiative neutron cross section is derived from the 352-keV γ-ray cross section and transition probability as σ0=2.394±0.019 b. A least-squares fit of the γ rays to the level scheme gives the Fe57 neutron separation energy Sn=7646.183±0.018 keV.