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In this thesis we discuss how one can derive the quantum spectral curve for the $\eta$-deformed AdS$_5 \times S^5$ superstring, an integrable deformation of the AdS$_5 \times $S$^5$ superstring with quantum group symmetry. This model can be viewed as a trigonometric version of the AdS$_5 \times $S$^5$ superstring, like the Heisenberg xxz spin chain is a trigonometric version of the xxx spin chain. Our derivation starts from the ground-state thermodynamic Bethe ansatz equations and discusses the construction of both the undeformed and the $\eta$-deformed quantum spectral curve. We reformulate it first as an analytic $Y$-system, and map this to an analytic $T$-system which upon suitable gauge fixing leads to a $\mathbf{P}\mu$ system, the quantum spectral curve. We then discuss constraints on the asymptotics of this system to single out particular excited states. At the spectral level the $\eta$-deformed string and its quantum spectral curve interpolate between the AdS$_5 \times $S$^5$ superstring and a superstring on "mirror" AdS$_5 \times $S$^5$, reflecting a more general relationship between the spectral and thermodynamic data of the $\eta$-deformed string. The thesis is set up such that it simultaneously reviews the development of the undeformed AdS$_5 \times $S$^5$ quantum spectral curve., Comment: 205 pages, lots of figures. PhD thesis, partially based on arXiv:1708.02894. Contains abstract in German. v2: updated references and fixed typos

These lectures are intended for graduate students who want to acquire a working knowledge of path integral methods in a wide variety of fields in physics. In general the presentation is elementary and path integrals are developed in the usual heuristic, non-mathematical way for application in many diverse problems in quantum physics. Three main parts deal with path integrals in non-relativistic quantum mechanics, many-body physics and field theory and contain standard examples (quadratic Lagrangians, tunneling, description of bosons and fermions, quantization of gauge theories etc.) as well as specialized topics (scattering, dissipative systems, spin \& color in the path integral, lattice methods etc.). In each part simple Fortran programs which can be run on a PC, illustrate the numerical evaluation of (Euclidean) path integrals by Monte-Carlo or variational methods. Also included are the set of problems which accompanied the lectures and their solutions., Comment: 183 pages (in German), 28 figures, Latex with amsmath, amssym; v2: typos corrected, chapters 1.7 and 2.3 expanded, 187 pages (in German), 29 figures; v3: corrections, more "Vertiefungen" (details), 198 pages (in German), 31 figures; v4: English version with additional part (solution of problems), 211 pages, 31 figures

After some brief biographical notes, Wolfgang Pauli's main contributions to general relativity, quantum theory, quantum field theory, and elementary particle physics are reviewed. A detailed description is given how Pauli descovered - before the advent of the new quantum mechanics - his exclusion principle., Comment: Opening lecture at the symposium: Wolfgang Pauli And Modern Physics, in honor of the 100th anniversary of Wolfgang Pauli's birthday, ETH (Zurich), May 4-6 2000; in German

The principles of General Relativity allow for a non-vanishing cosmological constant, which can possibly be interpreted at least partially in terms of quantum-fluctuations of matter fields. Depending on sign and magnitude it can cause accelerated or decelerated expansion at certain stages of cosmic evolution. Recent observations in cosmology seem to indicate that we presently live in an accelerated phase. We recall the history and fundamental issues connected with the cosmological constant and then discuss present evidences for a positive value, which causes the accelerated expansion., Comment: Text in german; LeTeX 2epsilon, 25 pages, 4 eps-figures