How to Grasp an Abstraction: Mathematical Models and Their Vicissitudes between 1830 and 1950. Introduction.- Knowing by Drawing: Geometric Material Models in 19th Century France.- Wilhelm Fiedler and his Models-the Polytechnic Side.- Models from the Nineteenth Century Used for Visualizing Optical Phenomena and Line Geometry.- Modeling Parallel Transport.- The great yogurt project: models and symmetry principles in early particle physics.- Interview with Myfanwy Evans: Entanglements on and Models of Periodic Minimal Surfaces.- The dialectics archetypes / types (universal categorical constructions / concrete models) in the work of Alexander Grothendieck.- 'Analogies,' 'Interpretations,' 'Images,' 'Systems' and 'Models': Some Remarks on the History of Abstract Representation in the Sciences since the Nineteenth Century.- Mappings, Models, Abstraction, and Imaging: Mathematical Contributions to Modern Thinking circa 1900.- Thinking with Notations: Epistemic Actions and Epistemic Activities in Mathematical Practice.- Matrices - Compensating the Loss of Anschauung .- Interview with Anja Sattelmacher: Between Viewing and Touching - Models and Their Materiality.- Interview with Ulf Hashagen: Exhibitions and Mathematical Models in the 19th and 20th Centuries.- Interview with Andreas Daniel Matt: Real-Time Mathematics.