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/