Integrability Supersymmetry and Coherent States : A Volume in Honour of Professor Véronique Hussin Chapter1. Curvature as an integrable deformation Chapter2. Trends in supersymmetric quantum mechanics Chapter3. Coherent states in Quantum Optics: An oriented overview Chapter4. Higher Order Quantum Superintegrability: a new Painlevé conjecture Chapter5. Supersymmetries in Schrodinger Pauli equationsand in Schrodinger equations with position dependent mass Chapter6. Nonlinear supersymmetry as a hidden symmetry Chapter7. Coherent and squeezed states: introductory review of basic notions properties and generalizations Chapter8. Trace Formulas Applied to the Riemann Function Chapter9. Real and complex energy non conserving particle number pairing solution Chapter10. Jacobi polynomials as su(2; 2) unitary irreducible representation Chapter11. Innite square well trigonometric Poschl Teller and other potential wells with a moving barrier Chapter12. Variational Method Applied to Schrodinger like Equation Chapter13. The Lippmann Schwinger formula and one dimensional models with Dirac delta interactions Chapter14. Hermite coherent states for quadratic refractive index optical media Chapter15. Analysis of CPN1 sigma models via soliton surfaces Chapter16. On the equivalence between Type I Liouville dynamical systems in the plane and the sphere Chapter17. Construction of partial dierential equations with conditional symmetries Chapter18. An Integro dierential Equation of the Fractional Form: Cauchy Problem and Solution Chapter19. Quasi integrability and some aspects of SU(3) Toda eld theory Chapter20. On some aspects of unitary evolution generated by non Hermitian Hamiltonians This volume shares and makes accessible new research lines and recent results in several branches of theoretical and mathematical physics among them Quantum Optics Coherent States Integrable Systems SUSY Quantum Mechanics and Mathematical Methods in Physics. In addition to a selection of the contributions presented at the 6th International Workshop on New Challenges in Quantum Mechanics: Integrability and Supersymmetry held in Valladolid Spain 27 30 June 2017 several high quality contributions from other authors are also included. The conference gathered 60 participants from many countries working in different fields of Theoretical Physics and was dedicated to Prof. Véronique Hussin—an internationally recognized expert in many branches of Mathematical Physics who has been making remarkable contributions to this field since the 1980s. The reader will find interesting reviews on the main topics from internationally recognized experts in each field as well as other original contributions all of which deal with recent applications or discoveries in the aforementioned areas