This proceedings volume is devoted to the interplay of symmetry and perturbation theory, as well as to cognate fields such as integrable systems, normal forms, n-body dynamics and choreographies, geometry and symmetry of differential equations, and finite and infinite dimensional dynamical systems. The papers collected here provide an up-to-date overview of the research in the field, and have many leading scientists in the field among their authors, including: D Alekseevsky, S Benenti, H Broer, A Degasperis, M E Fels, T Gramchev, H Hanssmann, J Krashil’shchik, B Kruglikov, D Krupka, O Krupkova, S Lombardo, P Morando, O Morozov, N N Nekhoroshev, F Oliveri, P J Olver, J A Sanders, M A Teixeira, S Terracini, F Verhulst, P Winternitz, B Zhilinskii.

Contents:

• On Darboux Integrability (I M Anderson et al.)
• Computing Curvature without Christoffel Symbols (S Benenti)
• Natural Variational Principles (D Krupka)
• Fuzzy Fractional Monodromy (N N Nekhoroshev)
• Emergence of Slow Manifolds in Nonlinear Wave Equations (F Verhulst)
• Complete Symmetry Groups and Lie Remarkability (K Andriopoulos)
• Geodesically Equivalent Flat Bi-Cofactor Systems (K Marciniak)
• On the Dihedral N-Body Problem (A Portaluri)
• Towards Global Classifications: A Diophantine Approach (P van der Kamp)
• and other papers