Linear Response and Equilibrium Dynamics -- Liouvillian Representation -- Hamiltonian Representation -- Genetic Code of Spectral Densities -- Recursion Method Illustrated -- Universality Classes of Dynamical Behavior -- Termination of Continued Fractions: Attempts at Damage Control -- Reconstruction of Spectral Densities from Incomplete Continued Fractions -- Transport of Spin Fluctuations at High Temperature -- Quantum Spin Dynamics at Zero Temperature.

In this monograph the recursion method is presented as a method for the analysis of dynamical properties of quantum and classical many-body systems in thermal equilibrium. Such properties are probed by many different experimental techniques used in materials science. Several representations and formulations of the recursion method are described in detail and documented with numerous examples, ranging from elementary illustrations for tutorial purposes to realistic models of interest in current research in the areas of spin dynamics and low-dimensional magnetism. The performance of the recursion method is calibrated by exact results in a number of benchmark tests and compared with the performance of other calculational techniques. The book addresses graduate students and researchers.