Mathematical Models with Singularities : A Zoo of Singular Creatures The book aims to provide an unifying view of a variety (a zoo) of mathematical models with some kind of singular nonlinearity in the sense that it becomes infinite when the state variable approaches a certain point. Up to 11 different concrete models are analyzed in separate chapters. Each chapter starts with a discussion of the basic model and its physical significance. Then the main results and typical proofs are outlined followed by open problems. Each chapter is closed by a suitable list of references. The book may serve as a guide for researchers interested in the modelling of real world processes Motion of charged particles in a line An electrostatically actuated micro electro mechanical system Forced Keplerian like systems Particles under a central force ﬁeld Bose Einstein condensates and signal transmission in optical ﬁbers Electron beam focusing by means of a periodic magnetic ﬁeld Point vortex dynamics Pumping effect in a pipe tank ﬂow conﬁguration Radial oscillations of a bubble in a time periodic pressure ﬁeld Radial oscillations of cylindrical and spherical shells A model for cell volume regulation