This book originates from K. Ribet's paper “On modular representations of $\mathrm {Gal}(\overline {\mathbf {Q}}/\mathbf {Q})$ arising from modular forms” (Invent. Math. 100, 1989), proving in particular that the Taniyama-Weil conjecture implies the Fermat conjecture. The first three papers are issued from conferences at a Seminar on that paper held in Orsay in 1987-88 and organised by G. Henniart and K. Ribet. The other four papers give new original results and generalisations of the present knowledge on the arithmetic of modular curves and Shimura curves. More specifically the first two papers by Raynaud and Illusie describe the reduction mod $p$ of the Néron model of the Jacobian $J_0(N)$ of the modular curve $X_0(N)$, at a prime $p$ dividing exactly $N$ (meaning $p|N$, but $p^2\!\!\not \!\!\;|\,N$) ; they give all necessary previsions concerning the Hecke and Galois actions on this reduction. The third paper, by Boutot and Carayol is a detailed exposition with complete proofs of drinfeld's method for obtaining the $p$-adic unifomisation of Shimura curves ( a result due to Čerednik). Such Shimura curves are used in a crucial way in Ribet's paper but are equally important in other aspects of number theory. The last for papers deal only with modular curves. Edixhoven's paper proves that the Hecke action on the group of components of the Néron model at $p$ of $J_0(N)$ is of Eisenstein type, for $p$ a prime dividing $N$, thereby generating results of Mazur and Ribet. Ling and Oesterlé's article deals with a related finite subgroup of $J_0(N)$, the Shimura subgroup, together with its Hecke and Galois action. Diamond's paper investigates the process (used by Ribet to complete his proof can be extended somewhat to level $pM$ where $p$ is prime to $M$, but not to the general situation. The introduction to the volume gives more details on the connection between the different papers and helps th reader to get the global picture.