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In this work, the fundamental elements of statistical mechanics underlying the simulation of the protein-ligand binding process, such as statistical ensembles and the concept of microscopic estimators of macroscopic observables and free energy, are summarized in a self consistent fashion. Particular attention is then devoted to the introduction of some mathematical tools that are used in atomistic simulations aimed at estimating binding affinities and free energy profiles, and to the illustration of the origins of the difficulties encountered in this endeavor.