I am going to start General Relativity by Wald. I will be using this as an opportunity to review some topology, analysis, differential geometry etc... This is prompted by watching some of Don Howard's wonderful lectures on Einstein. I also have a couple of other books on black holes that might be interesting -- one has a computation of how relativity is used in GPS. In the meantime I will wax philosophical about God knows what.
In the meantime I have been skimming a very nice book called 'Galileo's Muse', which details the artistic, literary, and philosophical context within which Galileo made his discoveries. The book credits Dante with discovering the 3-Sphere. Evidently a lot of people see this in the relationship between Hell and Paradise. There are passages in the Inferno that speak of how one knows whether one is at rest or moving. It seems as much or as little can be made of this as one wishes -- the book has not produced a document of Galileo saying 'I got my idea of transformations from Dante', but he did do a detailed analysis of the structure of Hell for a lecture he gave -- so it's not out of the question that the poem had a broader affect on Galileo. Interesting to point out here that Galileo(and for that matter, Einstein) made many of their greatest contributions as a result of 'thought experiments' -- who knows how the literary/artistic(especially for Galileo) contest may have influenced them. Einstein was very rigorously philosophical and traces his important thoughts to great figures like Hume.