In this talk, I will propose many-body invariants for the broad classes of topological insulators including Chern insulators, chiral hinge insulators, and multipole insulators. Unlike band indices which only work for non-interacting band insulators, the many-body invariants can detect non-trivial topology of quantum many-body wave functions hence applicable to fully interacting quantum systems. To this end, I will introduce several unitaries whose expectation values on many-body ground states serve as the invariants. I will explain that the unitaries detect the coefficients of the topological field theory, which are the defining characteristics of topological insulators. This allows one to develop a new way of evaluating Chern numbers, and also the many-body invariant for chiral hinge insulator. I will also show some numerical data on interacting systems using DMRG simulations for Chern insulator and self-consistent Hartree-Fock method for Hinge insulator. Furthermore, I will explain the many-body invariant for Chern insulator not only is readily implemantable to current DMRG schemes but also may significantly reduce the computing time for Chern number.