Maxima is a descendant of DOE Macsyma, which had its origins in the late 1960s at MIT. It is the only system based on that effort still publicly available and with an active user community, thanks to its open source nature. Macsyma was the first of a new breed of computer algebra systems, leading the way for programs such as Maple and Mathematica. Maxima itself is reasonably feature complete at this stage, with abilities such as symbolic integration, 3D plotting, and an ODE solver, but there is a lot of work yet to be done in terms of bug fixing, cleanup, and documentation.
WWW: http://maxima.sourceforge.net/