The Abel Symposia volume at hand contains a collection of high-quality articles written by the world's leading experts, and addressing all mathematicians interested in advances in deterministic and stochastic dynamical systems, numerical analysis, and control theory.

Facilitated Exclusion Process: Jinho Baik et al.- Stochastic Functional Differential Equations and Sensitivity to their Initial Path: D. R. Baños et al.- Grassmannian Flows and Applications to Nonlinear Partial Differential Equations: Margaret Beck et al.- Gog and Magog Triangles: Philippe Biane.- The Clebsch Representation in Optimal Control and Low Rank Integrable Systems: Anthony M. Bloch et al.- The Geometry of Characters of Hopf Algebras: Geir Bogfjellmo et al.- Shape Analysis on Homogeneous Spaces: a Generalised SRVT Framework: E. Celledoni et al.- Universality in Numerical Computation with Random Data. Case Studies, Analytical Results and Some Speculations: Percy Deift et al.- BSDEs with Default Jump: Roxana Dumitrescu et al.- The Faà di Bruno Hopf Algebra for Multivariable Feedback Recursions in the Center Problem for Higher Order Abel Equations: Kurusch Ebrahimi-Fard et al.- Continuous-Time Autoregressive Moving-Average Processes in Hilbert Space: Fred Espen Benth et al.- Pre- and Post-Lie Algebras: The Algebro-Geometry View: Gunnar Fløystad et al.- Extension of the Product of a Post-Lie Algebra and Application to the SISO Feedback Transformation Group: Loïc Foissy.- Infinite Dimensional Rough Dynamics: M. Gubinelli.- Heavy Tailed Random Matrices: How They Differ from the GOE, and Open Problems: Alice Guionnet.- An Analyst's Take on the BPHZ Theorem: Martin Hairer.- Parabolic Anderson Model with Rough Dependence in Space: Yaozhong Hu et al.- Perturbation of Conservation Laws and Averaging on Manifolds: Xue-Mei Li.- Free Probability, Random Matrices, and Representations of Non-Commutative Rational Functions: Tobias Mai et al.- A Review on Comodule-Bialgebras: Dominique Manchon.- Renormalization: a Quasi-Shuffle Approach: Frédéric Menous et al.- Hopf Algebra Techniques to Handle Dynamical Systems and Numerical Integrators: A. Murua et al.- Quantitative Limit Theorems for Local Functionals of Arithmetic Random Waves: Giovanni Peccati et al.- Combinatorics on Words and the Theory of Markoff: Christophe Reutenauer.- An Algebraic Approach to Integration of Geometric Rough Paths: Danyu Yang.