Maria Manuel Clementino is Full Professor at the Department of Mathematics and a member of the Research Centre for Mathematics of the University of Coimbra. Her main research contributions focus on the application of categorical methods in topology and algebra. She serves on the editorial board of several scientific journals and chairs the Steering Committee on Category Theory.Mai Gehrke is Senior Research Director in Computer Science at the French National Centre for Scientific Research (CNRS) working at the Department of Mathematics of Université Côte d’Azur in Nice, France. Her main contributions are in Stone duality, canonical extensions, and applications in logic and theoretical computer science. She is one of the founders of the TACL series. Jorge Picado is Full Professor at the Department of Mathematics and a member of the Research Centre for Mathematics of the University of Coimbra. His research interests include point-free topology and ordered structures. He is the co-author of the books Frames and Locales: Topology Without Points and Separation in Point-Free Topology, and serves on the editorial board of the journals Applied Categorical Structures, Order, and Quaestiones Mathematicae.

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• Chapter 1 Notes on duality theory.- Chapter 2 A Concise and Friendly Introduction to the Analysis of Algorithms for Continuous Nonlinear Optimization.- Chapter 3 Remarks on Non-formal Deformation Quantization of Poisson Manifolds.- Chapter 4 Linear and Nonlinear Fractional PDEs from Interacting Particle Systems.- Chapter 5 On Bi-Lipschitz Classification of Real and Complex Singularities.