Preface -- Asch/Bourget/Cortés/: Resonant behaviors for some time dependent quantum systems: some remarks -- Belmonte/Mǎntoiu: Continuity of Spectra in Rieffel’s Pseudodifferential Calculus -- Benguria: Stability of Matter -- Cornean/Purice: On the regularity of the Hausdorff distance between spectra of perturbed magnetic Hamiltonians -- De Nittis/Panati: The topological Bloch-Floquet transform and some applications -- Elgart/Krüger/Tautenhahn/Veselic: Discrete Schrödinger operators with random alloy-type potential -- Falomir/Pisani: Operator Domains and SUSY Breaking in a Model of SUSYQM with a Singular Potential -- Gorka/Prado/Reyes: Generalized euclidean bosonic string equations -- Klopp: Resonances for “Large” Ergodic Systems in One Dimension: a Review -- Klopp/Loss/Nakamura/Stolz: Understanding the Random Displacement Model: from Ground-State Properties to Localization -- Ojeda-Valencia/Villegas-Blas: On limiting eigenvalue theorems in semiclassical analysis -- de Oliveira/Verri: On norm resolvent and quadratic form convergences in asymptotic thin spatial waveguides -- Rebolledo: Equilibrium Analysis of a Dissipative Fermion System -- Richard/Tiedra de Aldecoa: A new formula relating localisation operators to time operators.

This volume contains surveys as well as research articles broadly centered on spectral analysis. Topics range from spectral continuity for magnetic and pseudodifferential operators to localization in random media, from the stability of matter to properties of Aharonov-Bohm and Quantum Hall Hamiltonians, from waveguides and resonances to supersymmetric models and dissipative fermion systems. This is the first  of a series of volumes reporting every two years on recent progress in spectral theory.