FlightGear is a sophisticated, realistic flight-simulator, created entirely by volunteers, and released as free, open-source GPL software, available for download here. FlightGear has a graphical user interface realistic enough for real-life pilot training, and mathematical flight models accurate enough for serious scientific research. FlightGear's free and open license also makes it great for educational exploration, or just for fun.
FlightGear can be expanded and improved by anyone interested in contributing. The complete project source code is available via Git, licensed under the GNU General Public License. FlightGear's open architecture encourages the exploration of a wide variety of flight simulator concepts, and has inspired a number of related projects.
FlightGear comes with a set of illustrated documentation, notably "The Manual", which is available as PDF and HTML.