The modern form of the shower was not invented until 1767, by William Feetham of London, whose initial design pumped water into a large basin above the head, before a chain was pulled to release the water. It was not until some time in 1810 that an anonymous inventor refined this design to be more similar to what is found in the modern world.
The idea of showers, despite not being properly designed and realized until the 18th century, had already been around for thousands of years.
Initially, mankind had used waterfalls for cleaning, with natural rainfall offering another way to clean without having to bathe in pools or lakes.
Ancient civilizations likely had very primitive versions of shower rooms, where servants would pour jugs of water over the heads of bathers.
The ancient Greeks also had a very basic form of shower, even using pumping techniques to raise the water above the head thanks to their use of lead piping as sewers. These showers were available to all, and even contained clothing hangers.
Because the Greeks, and later Romans, had such a good understanding of pumping water through pipes using pressure, it is arguable to say they invented the first forms of shower. This knowledge, however, was lost and it was not until the 18th century that similar techniques were rediscovered.