The open-source library, irbasis, provides easy-to-use tools for two sets of orthogonal functions named intermediate representation (IR). The IR basis enables a compact representation of the Matsubara Green's function and efficient calculations of quantum models. The IR basis functions are defined as the solution of an integral equation whose analytical solution is not available for this moment. The library consists of a database of pre-computed high-precision numerical solutions and computational code for evaluating the functions from the database. This paper describes technical details and demonstrates how to use the library. Program summary: Program Title: irbasis Program Files doi: http://dx.doi.org/10.17632/2fh88ynxm6.1 Licensing provisions: MIT license Programming language: C++, Python. External routines/libraries: numpy, scipy and h5py for Python library, HDF5 C library for C++ library. Nature of problem: Numerical orthogonal systems for Green's function Solution method: Galerkin method, piece-wise polynomial representation