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This book collects contributions to the Special Issue entitled "Symmetries in Quantum Mechanics and Statistical Physics" of the journal Symmetry. These contributions focus on recent advancements in the study of PT–invariance of non-Hermitian Hamiltonians, the supersymmetric quantum mechanics of relativistic and non-relativisitc systems, duality transformations for power–law potentials and conformal transformations. New aspects on the spreading of wave packets are also discussed.

non-Hermitian quantum dynamics --- unitary vicinity of exceptional points --- degenerate perturbation theory --- Hilbert-space geometry near EPs --- relativistic wave equation --- Klein–Gordon equation --- Dirac equation --- Proca equation --- supersymmetry --- quantum mechanics --- shape invariance --- curved space --- position-dependent mass --- supersymmetric quantum mechanics --- self-adjoint extensions --- infinite square well --- contact potentials --- power-law duality --- classical and quantum mechanics --- semiclassical quantization --- quark confinement --- spreading wave function --- scattering --- localization --- Klein–Gordon oscillator --- Green’s function --- semiclassical theories and applications --- classical general relativity --- n/a --- Klein-Gordon equation --- Klein-Gordon oscillator --- Green's function