The Roux Method is a relatively new method, invented by Gilles Roux and is becoming quickly popular. Unlike Fridrich and Petrus, the inventor of this method has gotten a sub-15 second average with it. It is also somewhat unique in that the last step is intuitive.
1. Build a 1x2x3 block, and hold it so that the U, M, and R slices are free.
2. Build a second 1x2x3 block on the right, so that U and M are free.
3. Solve the corners, ignoring the middle layer.
4. Solve the last six edges and the rest of the cube. This is done by orienting the edges, inserting the UL and UR edges, and then fixing the middle layer.
Like the Petrus method, the Roux method uses fewer moves than the popular Fridrich method. It is also more intuitive and requires fewer algorithms. Despite the M-heavy last step, it can also be extremely good for fewest moves competitions.
Block building can be difficult for a beginner to get used to. The reliance on r and M moves may also be difficult for some people, so much so that cubers who have trouble with M turns should probably not use this as their main method.