Could you provide recommendations for a good modern introductory textbook on differential geometry, geared towards physicists. I know physicists and mathematicians do mathematics differently and I would like to see how it is done by a physicists standard. I have heard Chris Ishams “Modern Diff Geometry for Physicists” is good in this respect but I don’t know how modern or at what level this is at. Theodore Frankels Geometry of Physics is mentioned a lot and highly regarded as being the most complete and comprehensive. I would like to get your opinions on what textbooks you think will be leading the way forward in physics classes on Diff Geom for Physicists?