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The purpose of this paper is to elucidate the multi-window method for spectral estimation and sinusoid detection. The multi-window method, devised by D.J. Thomson, has many features that distinguish it from other spectrum estimation techniques. It has an elegant derivation, starting from first principles and using optimality arguments. It lends itself to performance analysis and provides a built-in measure of its reliability. In contrast to Thomson's integral equation derivation, we use linear algebraic methods both to treat the problem and to develop the solution. In addition to the tutorial, we present an overview of published generalizations and analyses of the method.