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DDSCAT 7.2 is a freely available open-source Fortran-90 software package applying the discrete dipole approximation (DDA) to calculate scattering and absorption of electromagnetic waves by targets with arbitrary geometries and complex refractive index. The targets may be isolated entities (e.g., dust particles), but may also be 1-d or 2-d periodic arrays of "target unit cells", which can be used to study absorption, scattering, and electric fields around arrays of nanostructures. The DDA approximates the target by an array of polarizable points. The theory of the DDA and its implementation in DDSCAT is presented in Draine (1988) and Draine & Flatau (1994), and its extension to periodic structures in Draine & Flatau (2008). Efficient near-field calculations are enabled following Flatau & Draine (2012). DDSCAT 7.2 allows accurate calculations of electromagnetic scattering from targets with size parameters 2*pi*aeff/lambda < 25 provided the refractive index m is not large compared to unity (|m-1| < 2). DDSCAT 7.2 includes support for MPI, OpenMP, and the Intel Math Kernel Library (MKL). DDSCAT 7.2 supports calculations for a variety of target geometries (e.g., ellipsoids, regular tetrahedra, rectangular solids, finite cylinders, hexagonal prisms, etc.). Target materials may be both inhomogeneous and anisotropic. It is straightforward for the user to import new target geometries into the code. DDSCAT 7.2 calculates total cross sections for absorption and scattering and selected elements of the Mueller scattering intensity matrix for specified orientation of the target relative to the incident wave, and for specified scattering directions. DDSCAT 7.2 calculates E throughout a user-specified rectangular volume containing the target. A Fortran-90 code READNF to read E and P from files created by DDSCAT 7.2 is included in the distribution.