Quantum GIS (QGIS) is an Open Source GIS, licensed under the GNU General Public License. QGIS is an official project of the Open Source Geospatial Foundation (OSGeo). It runs on Linux, Unix, Mac OSX, Windows and Android and supports numerous vector, raster, and database formats and functionalities.
CUNY Hunter offers a practicum using QGIS; here is info and a manual.
Harvard’s Center for Geographic Analysis has quick guides and a do-it-yourself Workshop.
The SpatialThoughts blog maintains QGIS Tutorials.