Good old pulleys
A major improvement from the 4th century BC and still in use today, is the compound pulley: a combination of single pulleys in a block. The mechanical advantage equals the amount of pulleys used.
A crane with a triple pulley (a "Trispastos") has two pulleys attached to the crane and a free pulley suspended from them. It offers a mechanical advantage of 3 to 1. A crane with five pulleys in a similar arrangement (dubbed a "Pentaspostos") offers a mechanical advantage of 5 to 1.
Using a compound pulley a man can lift more than he is otherwise able to. If a single man pulling a rope can exert a force of 50 kg, he can raise (or lower) 150 kg using a Trispastos and 250 kg using a Pentaspostos. The same goes for the rope. A rope with a tensile strength of 50 kilograms can be used to lift (or lower) 150 kilograms if 3 pulleys are used, and 250 kilograms if 5 pulleys are used.
And you can pull the rope using winches and capstans