Friedrich and Petrus methods are quite common, as well as the Roux method. Some other methods are Heise, Zbroski-Brucem, and Vandebergh-Harris.
The Friedrich Method, sometimes called CFOP, was invented by Jessica Friedrich. It has 4 steps: Cross, First two layers (F2L), Orienting Last Layer (OLL), and Permuting Last Layer (PLL). There are many algorithms.
The Roux Method was invented by Gilles Roux. It has 4 steps, a 1x2x3 block, another one on the opposite side (F2B), orienting and permuting last four corners (can be done in one step called CxLL, as COLL, CELL... all work, even if CMLL are the best ones) and finally the last six edges (L6E or LSE), where you orient and permute the last remaining edges and finish the cube.