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This handbook consists of tabulations of the Slater-Koster parameters of 53 elements in the periodic table, including metals, semiconductors, and insulators. These parameters are derived by fitting to first principles self-consistent and scalar-relativistic band structure calculations using in all cases (except for Si, Ge, and Sn) the augmented plane-wave method. For the cubic materials four different sets of parameters are presented in this work, corresponding to the following representations: (1) three-center nonorthogonal, (2) three-center orthogonal, (3) two-center nonorthogonal, and (4) two-center orthogonal. For the hexagonal materials only two-center parameters are given.§For each element, figures showing the energy bands and densities of states resulting from the nonorthogonal three-center and two-center calculations for the cubic and hexagonal materials, respectively, are also included. For the 3d and 4d transition metals we present addition tabulations for cubic structures other than the usual ones.