Petrus Method

The Petrus Method, invented by Lars Petrus, is a blockbuilding method where the F2L is solved intuitively with no algorithms. Petrus was the second most popular speedcubing method behind Fridrich/CFOP; however other methods like ZZ and Roux are currently more popular.
Contents
The Steps
The following steps describe an approach suited for beginners, more advanced users might combine steps 1 and 2 and/or 5 and 6 (COLL) or use a Fridrich type last layer and do OLL and then PLL. If the fifth step is skipped the last layer can be solved with a 2GLL algorithm.
1. Build a 2x2x2 block anywhere on the cube.
2. Expand the 2x2x2 block to a 2x2x3 block; three ways are possible.
3. Fix the "bad edges" (in other words, orientate the remaining seven edges on the cube that have not been solved).
4. Finish the First Two Layers (F2L) by only turning 2 sides. The pure Petrus approach is to create a 1x2x2 block and expand it to a 1x2x3 block to finish off the F2L, not to solve the cross piece and two corner/edge pairs; two ways are possible. The lastlayer edges will orientate themselves automatically.
5. Permutate the lastlayer corners (put them in their correct places).
6. Orientate the lastlayer corners, making the whole last layer a solid colour.
7. Permutate the last layer edges, without disturbing the other pieces, to solve the cube.
Pros
 The Petrus Method uses fewer moves than the Fridrich method and most, if not all, other nonblockbuilding methods.
 It is more intuitive than the Fridrich method, and it requires far fewer algorithms.
 It requires fewer algorithms than some beginner methods (including the most popular one: Layer By Layer).
 If COLL is used as well, one can orientate and permutate the corners at the same time.
 The last layer can even be solved in one look with ZBLL or ZZLL, however this drastically increases the number of algorithms one must learn.
Cons
 It can be sometimes hard (especially for a beginner) to optimize block building, and it's difficult to keep consistently turning throughout the solve.
Petrus variations
There are several other substeps that can be used EJLS, WV, COLL, and ZBLL, which completes the entire last layer in a single algorithm.
Petrus as a Beginner Method
Used as a beginner method, Petrus requires much more intuition, but also involves learning fewer algorithms. For a tutorial, see the external links below.
External links
 Lars Petrus's tutorial
 Petrus Speed Website
 Speedsolving.com YouTube Beginner Petrus Tutorial
 YouTube: Petrus Tutorial by fallofshadows
 YouTube: Petrus Tutorial by CuberChris