Chapter 0 : Synopsis
Chapter 1 : Elliptic curves
Chapter 2 : Modular forms
Chapter 3 : Galois representations
Chapter 4 : The 3–5 trick
Chapter 5 : R=T
Chapter 6 : Commutative algebra
Chapter 7 : Deformation rings

In the first volume the modularity lifting theorem on Galois representations has been reduced to properties of the deformation rings and the Hecke modules. The Hecke modules and the Selmer groups used to study deformation rings are constructed, and the required properties are established to complete the proof. The reader can learn basics on the integral models of modular curves and their reductions modulo p that lay the foundation of the construction of the Galois representations associated with modular forms. More background materials, including Galois cohomology, curves over integer rings, the Néron models of their Jacobians, etc., are also explained in the text and in the appendices. --- summary provided by publisher