Every part of physics offers examples of non-stability phenomena, but probably nowhere are they so plentiful and worthy of study as in the realm of quantum theory. The present volume is devoted to this problem: we shall be concerned with open quantum systems, i.e. those that cannot be regarded as isolated from the rest of the physical universe. It is a natural framework in which non-stationary processes can be investigated. There are two main approaches to the treatment of open systems in quantum theory. In both the system under consideration is viewed as part of a larger system, assumed to be isolated in a reasonable approximation. They are differentiated mainly by the way in which the state Hilbert space of the open system is related to that of the isolated system - either by orthogonal sum or by tensor product. Though often applicable simultaneously to the same physical situation, these approaches are complementary in a sense and are adapted to different purposes. Here we shall be concerned with the first approach, which is suitable primarily for a description of decay processes, absorption, etc. The second approach is used mostly for the treatment of various relaxation phenomena. It is comparably better examined at present; in particular, the reader may consult a monograph by E. B. Davies.

1 / Quantum Kinematics of Unstable Systems.- 1.1. Is There Anything Left to Study on Unstable Systems?.- 1.2. Basic Notions.- 1.3. Small-Time Behaviour.- 1.4. The Inverse Decay Problem.- 1.5. Semiboundedness and Other Properties of the Energy Spectrum.- 1.6. Bounded-Energy Approximation.- Notes to Chapter 1.- 2 / Repeated Measurements on Unstable Systems.- 2.1. Decay Law in the Presence of Repeated Measurements.- 2.2. Periodically Structured Measuring Devices.- 2.3. A Model: Charged Kaons in a Bubble Chamber.- 2.4. Limit of Continual Observation and the 'Zeno's Paradox'.- Notes to Chapter 2.- 3 / Dynamics and Symmetries.- 3.1. Poles of the Reduced Resolvent.- 3.2. Friedrichs Model.- 3.3. Bounded Perturbations of Embedded Eigenvalues.- 3.4. Symmetries and Broken Symmetries.- 4 / Pseudo-Hamiltonians.- 4.1. Pseudo-Hamiltonians and Quasi-Hamiltonians.- 4.2. Maximal Dissipative Operators.- 4.3. Schrödinger Pseudo-Hamiltonians.- 4.4. The Optical Approximation.- 4.5. Non-unitary Scattering Theory.- Notes to Chapter 4.- 5 / Feynman Path Integrals.- 5.1. The Integrals that are not Integrals: a Brief Survey.- 5.2. Feynman Maps on the Algebra ?(?).- 5.3. Hilbert Spaces of Paths.- 5.4. Polygonal-Path Approximations.- 5.5. Product Formulae.- 5.6. More about Other F-Integral Theories.- Notes to Chapter 5.- 6 / Application to Schrödinger Pseudo-Hamiltonians.- 6.1. Feynman-Cameron-Itô Formu la.- 6.2. The Damped Harmonic Oscillator.- 6.3. The 'Feynman Paths'.- Notes to Chapter 6.- Selected Problems.