FINUFFT is a set of libraries to compute efficiently three types of nonuniform fast Fourier transform (NUFFT) to a specified precision, in one, two, or three dimensions, on a multi-core shared-memory machine. The library has a very simple interface, does not need any precomputation step, is written in C++ (using OpenMP and FFTW), and has wrappers to C, fortran, MATLAB, octave, and python.