Everything you wanted to know about abstract algebra, but were afraid to buy
Sage is an open-source program for doing mathematics and is the ideal companion to Abstract Algebra: Theory and Applications. Sage is designed to be a free, open source alternative to Magma, Maple, Mathematica and Matlab. It includes many mature and powerful open-source tools for mathematics, such as GAP for group theory. With a strength in number theory, Sage also has excellent support for rings and fields.
Rob Beezer has contributed extensive material about studying abstract algebra concepts with Sage, and instruction in the use of Sage itself. Coverage includes every chapter but one (
Matrix Groups and Symmetry) with 121 classroom-tested exercises, ranging from very computational to open-ended guided explorations. This material is illustrated with 710 examples of Sage code, which are executable and editable, via the free Sage Cell server in the online HTML version. Static versions are contained in the electronic PDF (but not the print edition). These examples are run through automated testing every six months with the latest version of Sage, so are highly reliable.
Note (2015/07/29): Work is underway to provide the Sage material in various formats. Check back here, but in the interim, see links from the Public Beta.
There was once a tutorial here, and we have left the PDF available. It is now obsolete and is no longer being maintained. If you have a link pointing here, you might wish to adjust the description of what is actually available.