The hyperbolic nature of the Einstein equations is well-established and has been used in many different contexts. More recently, the double null foliation has proven to be a powerful tool for quantitative analysis of the Einstein equations. It has been used to answer many questions in general relativity, including stability problems and trapped surface formation. However, the local existence problem for the Einstein equations in a double null foliation has never been treated fully in its own right. In this talk, we discuss the linear theory of hyperbolic systems in a double null foliation.