This monograph is dedicated to the presentation of the Gradient Discretisa- tion Method (GDM) and of some of its applications. It is intended for masters students, researchers and experts in the field of the numerical analysis of par- tial differential equations. The GDM is a framework which contains classical and recent discretization schemes for diffusion problems of different kinds: linear or non linear, steady- state or time-dependent. The schemes may be conforming or non conforming and may rely on very general poygonal or polyhedral meshes. In this monograph, the core properties that are required to prove the conver- gence of a GDM are stressed, and the analysis of the method is performed on a series of elliptic and parabolic problems, linear or non-linear, for which the GDM is particularly adapted. As a result, for these models, any scheme entering the GDM framework can then be known to converge. Appropriate tools are then developed so as to easily check whether a given scheme satisfies the expected properties of a GDM. Thanks to these tools a number of methods can be shown to enter the GDM framework: some of these methods are classical, such as the conforming Finite Elements, the Raviart- Thomas Mixed Finite Elements, or the P1 non-conforming Finite Elements. Others are more recent, such as the Hybrid Mixed Mimetic or Nodal Mimetic methods, some Discrete Duality Finite Volume schemes, and some Multi-Point Flux Approximation schemes.