LMCF

The LMCF Method, or Low Movecount Corners First, was invented by Eric Fattah. It is an improved version of the Corners First Method. Because of its low movecount, the method can easily be used to get sub10 singles with only 45 TPS.
Contents
The Steps
1. Solve the corners with full EG. Make sure the centers are solved relative to the corners.
2. Transition Phase  This step doesn't require any algorithms, but it is very important. During the transition phase you solve 1 or 2 of the edges in the top layer while scanning the E slice for your E2L (Edges of the 2 Layers) pairs.
3. Solve all but two of the remaining E2L pairs. In order to maintain a low movecount, solve you E2Ls in pairs or triplets. This step is done intuitively. By the end of this step the E slice will have become the M slice, and the U layer the R layer.
4. Solve the remaining 2 edges on the right/left faces while orienting the edges in the M slice. This step can be completed in as little as 8 algorithms or intuitively.
5. Permute the remaining M slice edges. There are only 3 cases, and they all are solvable in 5 moves or less.
Pros
 Low Movecount (~45 moves STM)
 Gradual progression from beginner to advanced
 2x2 step is very optimized
 Algorithms are often shorter and easier to learn than ZBLLs or OLLCPs
 Skips on steps allow for very fast singles
 Algorithm carryover with 2x2
Cons
 Can be difficult to understand for beginners
 High algorithm count
 Very reliant on slice moves, making it hard to use for big cubes
 Little support from high end cubers
 Not good for use in OH and Feetsolving because of reliance on slice moves.
 Difficult to achieve high TPS due to reliance on intuition during E2L