  Topological electronic flatten bands near or at the Fermi level are a
promising avenue towards unconventional superconductivity and correlated
insulating states. However, the related experiments are mostly limited to the
engineered materials, such as moire systems. Here we present a catalogue of all
the three-dimensional stoichiometric materials with flat bands around the Fermi
level that exist in nature. We consider 55,206 materials from the Inorganic
Crystal Structure Database catalogued using the Topological Quantum Chemistry
website which provides their structural parameters, space group (SG), band
structure, density of states and topological characterization. We combine
several direct signatures and properties of band flatness to a high-throughput
analysis of all crystal structures. In particular, we identify materials
hosting line-graph or bipartite sublattices - either in two or three dimensions
- likely leading to flat bands. From this trove of information, we create the
Materials Flatband Database website, a powerful search engine for future
theoretical and experimental studies. We use it to extract a curated list of
2,379 materials, with among them 345 promising candidates, potentially hosting
flat bands whose charge centers are not strongly localized on the atomic sites.
We showcase five representative materials: KAg[CN]2 in SG 163 $(P\bar{3}1c)$,
Pb2Sb2O7 in SG 227 $(Fd\bar{3}m)$, Rb2CaH4 in SG 139 $(I4/mmm)$, Ca2NCl in SG
166 $(R\bar{3}m)$ and WO3 in SG 221 $(Pm\bar{3}m)$. We provide a theoretical
explanation for the origin of their flat bands close to the Fermi energy using
the $S$-matrix method introduced in a parallel work [Calugaru et al., Nature
Physics 18, 185 (2022)].
