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Repeaters are
fairly simple. A Redstone signal can only travel 16 blocks before it gets too weak to power anything (you'll see the color slowly fade away from a line of redstone connected to an active power source like a redstone torch or a lever). A repeater "restarts" the signal, and also delays it by one to four "ticks", depending on the setting. (Default is 1 tick, each time you right-click increases the delay by one tick, if you right-click a repeater on maximum delay it will cycle back to 1 tick.) The only real quirk about repeaters is, they can't power redstone down "stair steps" like redstone wire can.
That's the basic version, it gets more complex from there of course, but just with that knowledge you can do plenty of simple circuits. Just remember, repeaters: a.) extend a redstone signal that's getting weak (indicated by fading color in the wires), and b.) add a small, customizable delay of 1-4 "ticks" to the circuit.
