The ZB System is a very demanding brute force system for solving the Last Layer in fewer moves than the standard 2-look LL (OLL + PLL). It is named after the cubers who first publicised the idea of the system, Zbigniew Zborowski of Poland, and Ron van Bruchem of the Netherlands.
The method is identical to the standard CFOP system, up until the final F2L pair. Whilst solving the 4th pair, you also orient the edges of the LL. Secondly, you solve everything that remains, which includes Orientation of Corners, Permutation of Corners, and Permutation of Edges. Neither of these steps are for the faint-hearted, with a combined total of almost 800 algorithms. A big plus point of this system however, is that recognition of the cases is fairly straightforward, as opposed to recognition of the 1211 cases which make up a full 1-look LL.
I have included sections on the ZBF2L, and the ZBLL, assuming you already have the knowledge to solve the Cross + standard F2L. Please bear in mind it will probably take me a lonnnng time to include all algorithms!
Best of Luck! - DanH
The idea here is to solve the final F2L pair and simultaneously orient the LL edges. There are 41 cases for the standard F2L, but orienting LL edges multiplies this up to 306 cases. There are other, more simple ways to complete this step, but that are also less efficient. One of the alternatives is the VHF2L, which is described here.
This step is the jewel in the crown of the ZB system. With the LL edges correctly Oriented, you can go on to finish the cube by Orienting and Permuting the LL corners, and Permuting the LL edges, all in one step. There is only the small matter of 493 cases to learn!