Since the question is a bit too general while not specifying exactly what you need, I would consider a few points. It is resonable to look at : 

 - [The Mathematica GuideBooks][1] by M.Trott, especially "Symbolics". 

On the same internet site there is (also helpful in differential geometry) : 

 - [a talk about doing physics with Mathematica 6][2]

another interesting thing by the same author :

 - [Riemann Surfaces of Inverse Trigonometric Functions][3]

Obviously you could find many helpful things here at the Wolfram Demonstrations :

 - [Differential Geometry][4]

Next it would be very helpful to look at this article in the Mathematica Journal by Murray Eisenberg and David J. M. Park, Jr. :

 - [Visualizing Complex Functions with the Presentations Application][5]

One should also look at the geometry section of

 - [Wolfram Library Archive][6]

If you are looking for a package for tensor calculus, especially in General Relativity, the best choice is xAct made by José M. Martín-García (as far as I know he actually develops built-in functionality for the next version of Mathematica): 

 - [Efficient tensor computer algebra for Mathematica][7]

 


 [1]: http://www.mathematicaguidebooks.org/
 [2]: http://www.mathematicaguidebooks.org/talks/IMS_2008.zip
 [3]: http://demonstrations.wolfram.com/RiemannSurfacesOfInverseTrigonometricFunctions/
 [4]: http://demonstrations.wolfram.com/topic.html?topic=Differential%20Geometry&limit=20
 [5]: http://www.mathematica-journal.com/2011/10/visualizing-complex-functions-with-the-presentations-application/
 [6]: http://library.wolfram.com/infocenter/BySubject/Mathematics/Geometry/
 [7]: http://www.xact.es/