If you have not had a course in GR before nor a firm grounding in differential geometry (tensor calculus), then I strongly recommend Thomas Moore's excellent book A General Relativity Workbook, University Science Books, 2013, ISBN 978-1-891389-82-5,
http://www.uscibooks.com/moore.htm,
http://www.amazon.com/General-Relativity-Workbook-Thomas-Moore/dp/1891389823
This book does not have any associated Mathematica notebooks; however, it is easy to implement Mathematica where it is needed, especially for things like orbital precession, and the deflection of photons. I have several notebooks drawn from Moore's book that I would be willing to share.