Preface; List of contributors; 1. A semi-stable case of the Shafarevich conjecture V. Abrashkin; 2. Irreducible modular representations of the Borel subgroup of GL2(Qp) L. Berger and M. Vienney; 3. p-adic L-functions and Euler systems: a tale in two trilogies M. Bertolini, F. Castella, H. Darmon, S. Dasgupta, K. Prasanna and V. Rotger; 4. Effective local Langlands correspondence C. J. Bushnell; 5. The conjectural connections between automorphic representations and Galois representations K. Buzzard and T. Gee; 6. Geometry of the fundamental lemma P.-H. Chaudouard; 7. The p-adic analytic space of pseudocharacters of a profinite group and pseudorepresentations over arbitrary rings G. Chenevier; 8. La série principale unitaire de GL2(Qp): vecteurs localement analytiques P. Colmez; 9. Equations différentielles p-adiques et modules de Jacquet analytiques G. Dospinescu.