The Petrus Method, invented by Lars Petrus, is a block-building 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.
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.
3. Fix the "bad edges" or orient 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.
5. Permute the last layer corners, or put them in their proper places (they do not have to be oriented.)
6. Orient the last layer corners, making the whole last layer a solid color.
7. Permute the last layer edges, without disturbing the other pieces, to solve the cube.
The Petrus Method uses fewer moves than the Fridrich method and most other non-block-building methods. It is more intuitive than the Fridrich method, and it requires far less algorithms. If COLL is used as well, you can orient and permute 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.
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 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.