Hi everyone, I was wondering if I could some advice from anyone who has some experience with higher level general relativity. Any help would be greatly appreciated! Some background: I'm currently working through Robert Wald's General Relativity and am struggling a lot with the "advanced topics" chapters. For example, starting with the chapter on causality he begins to introduce notions from topology that I'm not really familiar with. The only topology that I have seen is from the second chapter of Rudin's Principles of Mathematical Analysis and that was from a course that I took two years ago in analysis. The appendix on it doesn't really help me any. In fact, I'm also finding it hard to follow every appendix and the chapter on spinors. In other words, everything after chapter 6! Even reading the same topics in the appendices in Sean Carrolls book leaves me scratching my head. It's pretty clear that I don't have the proper background in topology and differential geometry (which I took a semester of, but at a lower level than used in these books.) I eventually want to move onto more advanced books (Hawking & Ellis, Penrose & Rindler, De Felice & Clarke etc). However, I don't want to approach them with a shaky (and even sketchy) understanding of the mathematics involved. My goal in working through Wald is to understand everything in it thoroughly and patch up things that I missed in Schutz' and Carroll's books. With this in mind, I want to set aside GR for the time being and focus more on becoming competent with the mathematical machinery. My question is: What books on topology and differential geometry (and even group theory) focus on what has the most application to GR? I see a lot of people recommend Munkres, but he doesn't seem to cover very much on manifolds. I have Barret O'Neill's Elementary Differential Geometry, but again there doesn't seem to be a whole lot overlap between it and what is covered in GR. I'm looking for something at the advanced undergraduate or graduate level with a lot of worked problems (I can't emphasize that enough!) The only books I may have found so far are the ones by John M. Lee (Introduction to Topological Manifolds and Introduction to Smooth Manifolds.) Does anyone have any experience with them? Sorry that this post became so long - I thought that if I listed specifics of what I want to study in GR, it would be easier to recommend an appropriate text! Thanks!