Hairer and Wanner (Solving Ordinary Differential Equations) is the classic if you want a graduate level understanding of the mathematical details of all the different methods, but it is incredibly dense (thorough understanding of both volumes will take months to years). If you want a more approachable reference, I would recommend https://book.sciml.ai/ (specifically chapters 7-9) which skips over most of the detail on how to construct ODE solvers but covers quite well the methods that tend to be used in practice.