Developing Intuition for the Monster Group

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Here is my context. I recently finished my undergraduate studies and am moving on to graduate work. I have learned up to and including the Sylow theorems, group actions, and conjugacy classes. Over two summers, I tried to read Conway's Sphere Packings, Lattices and Groups, as well as Wilson's Finite Simple Groups; however, I did not get far in either as my prerequisite knowledge seemed lacking.

So far, I've learned how to construct the extended Golay Code from the hexacode (using the MOG), and the Leech Lattice from the extended Golay Code. Parker's Loop is a little beyond my understanding as well as the Golay Cocode.

My goal is it learn enough to have a relatively modern understanding of the monster group even if it takes me several years or longer. Currently, I am lost on how to pursue this goal. I do not know which books to read and in what order. I am looking for a step by step guide (or a way to learn how to best make my own) in terms of books to read (preferably in an ascending order of difficulty and relevance to the monster group). Any tips and warnings from those who have a modern understanding would be helpful as well.

Thanks for the help.