Hi, I'm looking to apply for theoretical physics PhDs in the coming year and have been recommended getting a little more mathematics under my belt. I have already done a bit of differential geometry in my G.R. course but I don't think it went into enough depth to be useful outside of what we covered. I'm hoping to develop at least a qualitative understanding of some of the ideas currently used in field theories, string theories etc. so I have something to talk about at interviews : p With this in mind I was wondering if Geometrical Methods of Mathematical Physics by Schutz would be a good starting point for getting a little more abstract maths? Are there any other books people would recommend to get started? Thanks very much.