A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.

Integrable systems: a celebration of Emma Previator's 65th birthday Ron Donagi and Tony Shaska; 1. Trace ideal properties of a class of integral operators Fritz Gesztesy and Roger Nichols; 2. Explicit symmetries of the Kepler Hamiltonian Horst Knörrer; 3. A note on the commutator of Hamiltonian vector fields Henryk ¿ö¿dek; 4. Nodal curves and a class of solutions of the Lax equation for shock clustering and Burgers turbulence Luen-Chau Li; 5. Solvable dynamical systems in the plane with polynomial interactions Francesco Calogero and Farrin Payandeh; 6. The projection method in classical mechanics A. M. Perelomov; 7. Pencils of quadrics, billiard double-reflection and confocal incircular nets Vladimir Dragovi¿, Milena Radnovi¿ and Roger Fidèle Ranomenjanahary; 8. Bi-flat F-manifolds: a survey Alessandro Arsie and Paolo Lorenzoni; 9. The periodic 6-particle Kac-Van Moerbeke system Pol Vanhaecke; 10. Integrable mappings from a unified perspective Tova Brown and Nicholas M. Ercolani; 11. On an Arnold-Liouville type theorem for the focusing NLS and the focusing mKdV equations T. Kappeler and P. Topalov; 12. Commuting Hamiltonian flows of curves in real space forms Albert Chern, Felix Knöppel, Franz Pedit and Ulrich Pinkall; 13. The Kowalewski top revisited F. Magri; 14. The Calogero-Françoise integrable system: algebraic geometry, Higgs fields, and the inverse problem Steven Rayan, Thomas Stanley and Jacek Szmigielski; 15. Tropical Markov dynamics and Cayley cubic K. Spalding and A. P. Veselov; 16. Positive one-point commuting difference operators Gulnara S. Mauleshova and Andrey E. Mironov.