Use at your own risk.
This tutorial seeks to teach you how to refresh a redstone signal with absolutely no delay. It involves clever uses of BUD-powered pistons.
How To Make One
The most common instant repeater requires a pulse at least four redstone ticks long. It is made by having a redstone signal powering a block that powers a sticky piston on top of it, facing the direction of the rest of the signal. This sticky piston has a redstone block on its face. The block that is powered is also attached to a sticky piston, but it's facing the opposite direction and is diagonally below the redstone block, such that the block can power the top piston when the bottom piston is extended. The rest of the signal is powered when the redstone block is extended forward.
It works by BUD-powering the bottom piston. When the pulse is received, the top piston starts moving. This updates the bottom piston, causing it to retract at exactly the same time as the top one is extending, thus depowering the top piston. This 0-ticks the top piston. The redstone block is now powering the bottom piston, so it extends. The block on its face comes back to its original position, but the start of the redstone line is still powered. This powers the top piston, and retracts the redstone block, depowering the redstone line at the end and BUD-powering the bottom piston. In real time, it looks like the contraption does an "inchworm." This produces pulses that are two redstone ticks long, which means that they can be chained together.
Any time a redstone signal needs to get somewhere instantly, an instant repeater can come in useful. Here is a common scenario:
You have several flying machines that all need to move at the same time, or else they will get stuck to each other and break. This situation can be resolved by starting them all up at exactly the same time, using redstone. Instead of using an ordinary repeater to keep the signal going (which adds 1 tick of delay, possibly breaking the machines), use an instant repeater to ensure that they stay synchronized.