Two-dimensional (2D) topological materials host symmetry-protected, disorder-robust edge states central to quantum technologies. Yet they remain scarce compared with their 3D counterparts. We adapted the topological quantum chemistry formalism to layer groups and studied the band topology of 8872 entries from the computational materials databases C2DB and MC2D. We found 4073 topological or obstructed entries, including 905 topological insulators and 1003 obstructed atomic insulators, greatly expanding the library of such materials in two dimensions. Detailed electronic and topological properties of all materials have been compiled into a Topological 2D Materials Database (2D-TQCDB), and the edge states of selected new materials have been studied in detail. Our methodology has been implemented in publicly available programs, designed to study the topology of any nonmagnetic monolayer or multilayer material.