Maxima is a free version of the computer algebra system Macsyma. It is available for various platforms and can be downloaded from http://maxima.sourceforge.net/download.shtml. The user interface of Maxima is less impressive than that of Macsyma, but the mathematical power of Maxima is very impressive.
The once famous computer algebra system Macsyma was developed in the years 1966 - 1971 at the MIT Laboratory for Computer Science. The MIT was doubtlessly an ideal place to do that work: It was there that Lisp was created and in the late sixties the leading Lisp experts worked at the MIT.
The success story of Macsyma ended quite abruptely in 1999, when the Macsyma Inc. was sold and the support for Macsyma discontinued.
Derivative work of Macsyma was done at several places. Maxima is the work of William F. Schelter (see: http://en.wikipedia.org/wiki/Bill_Schelter), a former professor at the University of Texas at Austin. He supported Maxima from 1982 until his untimely death in July 2001.