I finished it but certainly can't claim to have understood everything in it. I read it on and off for several weeks so it definitely took some effort for me. I

I finished it but certainly can't claim to have understood everything in it. I read it on and off for several weeks so it definitely took some effort for me. It's an incredibly dense book. There's nothing else out there quite like it. Penrose also has a pretty idiosyncratic method of presenting ideas. This means that sometimes you can't cross-reference his explanations even if you want to. He covers some exotic and nonstandard topics as well. I haven't personally seen his diagrammatic notation for tensor algebra anywhere else, for instance. And the book was my first and only exposure to hyperfunctions. The "trick", honestly, is to already have some prior exposure to most of the tricky mathematical ideas, like differential forms and fiber bundles. I was by no means an expert on differential geometry but I'd been exposed to it a few times as an undergraduate. The other "trick" is simply not to skip around. I was tempted at first to browse and read whatever topics interested me; this book is not structured that way. He constantly references backwards in the book, and even if you know the mathematical material some of his references can be confusing. This is probably the greatest weakness of the book. For instance, gauge connections aren't really covered fully in any single section of the book. They're discussed briefly in the chapter on fiber bundles, and then again in the chapter on electromagnetism, and then again I believe in the chapter on quantum mechanics, and none of these discussions is complete, but they are if taken together.