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The purpose of these notes is to give a fairly narrow but thoroughintroduction to the spectral analysis of Hamiltonians and standard Liouvilleansdescribing finite dimensional small systems linearly coupled to a scalarmassless field or reservoir. The Hamiltonians describe the system at zerotemperature, and the standard Liouvillean implements unitarily the dynamics ofthe system at positive temperature.  We focus our attention on results valid at arbitrary coupling strength andwhose proofs are purely operator theoretic, i.e. for the standard Liouvilleandoes not make use of the underlying modular structure. This means thatimportant structure results at positive temperature that does not seem to havea purely operator theoretic proof will only be reviewed.

Fully Coupled Pauli-Fierz Systems at Zero and Positive Temperature