Nonlinear PDE. Singularities, Propagation, Applications -- From Wave to Kleinโ{128}{148}Gordon Type Decay Rates -- Local Solutions to Quasi-linear Weakly Hyperbolic Differential Equations -- An Approach to a Version of the S(M, g)-pseudo-differential Calculus on Manifolds -- Spectral Invariance and Submultiplicativity for the Algebras of S(M, g)-pseudo-differential Operators on Manifolds -- Domain Perturbations and Capacity in General Hilbert Spaces and Applications to Spectral Theory -- An Interpolation Family between Gabor and Wavelet Transformations. Application to Differential Calculus and Construction of Anisotropic Banach Spaces -- Formes de torsion analytique et fibrations singuliรจres -- Regularisation of Secondary Characteristic Classes and Unusual Index Formulas for Operator-valued Symbols