In this thesis we consider a canonical analysis of double null General Relativity. We start with an introduction to Lagrangian and Hamiltonian dynamics, which introduces many of the techniques that are used throughout this thesis. Then in chapter 2 we introduce the canonical quantisation process, and perform the analysis on electromagnetism and General Relativity to help clarify the steps involved. In chapter 3 we introduce the double null formation of General Relativity. From this understanding we calculate the canonical analysis of thesis description. The complexity of the resulting constraints provides the motivation to introduce Ashtekar variables, the topic of chapter 4. This chapter also introduces SO(3) variables. The new variables are then used in the canonical analysis of the double null description of General Relativity. Two different methods are considered and while the resulting constraint algebra remains the same, the two methods have different advantages.