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NFFT is a software library, written in C, for computing non-equispaced fast Fourier transforms and related variations. It implements the following transforms: 1. Non-equispaced fast Fourier transform (NFFT) - forward transform (NFFT), i.e. frequency to time/space domain - adjoint transform (adjoint NFFT), i.e. time/space to frequency domain 2. Generalisations - to arbitrary nodes in time and frequency domain (NNFFT) - to real-valued data, i.e. (co)sine transforms, (NFCT, NFST) - to the sphere S^2 (NFSFT) - to the rotation group (NFSOFT) - to the hyperbolic cross (NSFFT) 3. Generalised inverse transformations based on iterative methods, e.g. CGNR/CGNE