I have taken an undergraduate course in GR via Thomas Moore's A General Relativity Workbook. To prepare for a research experience, I have been advised to take a GR course, so I will be refreshing myself on the work I did through this course. I would like to supplement my work with differential geometry by studying from one of the following books:
Riemannian Geometry by Manfredo Perdigão do Carmo (unfortunately don't have his earlier Curves and Surfaces book),
Differential Geometry and Its Applications by John Opera,
Elements of Differential Geometry by Millman and Parker,
notes on Differential Geometry by Hicks,
Elementary Differential Geometry by Barrett O'Neil,
An Introduction to Differentiable Manifolds and Riemannian Geomtry by Boothew,
as well as the graduate-level general relativity texts,
General Relativity by Wald, and
Gravitation by Misner, Thorne, and Wheeler.
Any recommendations of a favorite among these?