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xAct has more than 500 A4-pages of documentation, distributed in the different packages, and accessible in different formats. Keeping documentation up to date is difficult, and I ask for help in reporting outdated pages and undocumented (or badly documented) features of the system.


This is a Wolfram Mathematica slideshow I use in my introductory talks. It is a simple and slow introduction to the system:

Notes for a course on xTensor, held in Paris in April 2009:

See also the xAct Course held in Prague in 2018 by Alfonso García-Parrado, the introduction to xAct by Teake Nutma, or the introductory tutorial by Jolyon Bloomfield.

xAct tutorial in ICERM 2020: video (or in youtube), full notebook of the talk, smaller notebook without outputs.

xAct intro (Nov 23, 2022) in youtube, notebook of the talk.

Video course by Konstantinos Anagnostopoulos: xAct for the General Theory of Relativity.

Video of a talk by Barry Wardell: Tensor algebra made easy with Mathematica.

Tutorials on Mathematica and xAct presented by Zu-Cheng Chen at Guangzhou University in 2019.

Videos of a series of talks by xAct developers in March 2024, to celebrate 20 years of xAct.

Check out the great collection of contributed xAct example notebooks, and add your own examples to help others learning to use xAct!


Introductory file xCoreDoc:


Introductory file xPermDoc:


Introductory file xTensorDoc:

Reference guide xTensorRefGuide:


Introductory file xCobaDoc:


Introductory file InvarDoc:


Introductory file SpinorsDoc:

NP and GHP Formalisms:


Introductory file SymManipulator: