Cut the limes into thin slices. Put the peppermint leaves and lime wedges in a glass container, e.g., a baking dish, layer.
Bring the sugar to the boil in the water, stirring until it has dissolved. Let the sugar water cool down and pour over the peppermint-lime mixture. Let everything stand in the sun for 2 days if possible.
Strain after the 2 days, e.g., through a cheesecloth or a thin kitchen towel and fill into bottles.
Mixed with cold mineral water you have a refreshing summer drink.