This chapter reviews the theory of correlation functions for classical Hamiltonian systems as a method for a statistical description of the dynamics. Mathematical tools are introduced, which provide a connection of the description in the time domain with that in the frequency domain. The results of linear response theory are summarized; they relate the mathematical description to quantities relevant for the discussion of experiments. The concept of arrested parts of correlations is explained. The Zwanzig–Mori equations of motion are derived as a reformulation of the correlation functions in terms of relaxation kernels. The latter are fluctuating-force-correlation functions defined for a reduced dynamics. The chapter discusses how the structure of these equations can be used as a framework for the construction of correlation-function models.
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