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In this volume the fundamental theory of open quantum systems is revised in the light of modern developments in the field. A unified approach to the quantum evolution of open systems is presented by merging concepts and methods traditionally employed by different communities, such as quantum optics, condensed matter, chemical physics and mathematical physics.
The mathematical structure and the general properties of the dynamical maps underlying open system dynamics are explained in detail. The microscopic derivation of dynamical equations, including both Markovian and non-Markovian evolutions, is also discussed. Because of the step-by-step explanations, this work is a useful reference to novices in this field. However, experienced researches can also benefit from the presentation of recent results.

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Introduction.- Mathematical tools.- Time evolution in closed quantum systems.- Time evolution in open quantum systems.- Quantum Markov process: mathematical structure.- Microscopic description: Markovian case.- Microscopic description: non-Markovian case.- Conclusion.

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From the reviews:
"The book is a monograph dealing with a selection of topics in open quantum systems theory. Its particular aim with respect to other publications is to connect the results to a more solid mathematical background, so that most results are directly proven, even though proofs are usually restricted to a finite-dimensional setting to keep matters simple. ... The monograph is written in a clear and concise style and provides a compact introduction to the subject ... ." (Bassano Vacchini, Mathematical Reviews, Issue 2012 j)

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