Warp Drive System
Warp drive is by far the most widespread method of faster than light travel used in the alpha quadrant. Invented in 2063 by Zephram Cochrane of Earth (and later of Alpha Centuri), the first of his warp drives used a fission reactor to create a low energy plasma stream. This was split into two and directed through a pair of warp coils to produce a field around the ship which propelled it - briefly - faster than the speed of light.
Humans subsequently sold warp drive ships to many other cultures, and this technology has become common within the quadrant with over 2,000 species using it. The present day state of the art is not fundamentally different from Cochranes original system; ships today generally use matter / antimatter reactors rather than fusion ones, and dilithium has allowed more advanced power systems. The warp coils themselves have also become more numerous and complex in design.
For the future, many developments are possible. Over a century since it was first envisaged, transwarp drive remains seemingly just beyond the reach of Federation science. Other lines of research involve co-axial warp cores, which allow instantaneous travel over sizeable distances, and slipstream technology, which could theoretically allow travel at hundreds of light years per second. If this latter technology proves successful, it would make travel on an intergalactic scale easily feasible.