Plants have grown in our lakes and oceans from the beginning of time but, as a farming practice, many believe it started in the ancient city of Babylon. The Hanging Gardens of Babylon are believed to be the first successful attempts to grow plants hydroponically.
Along the Nile, hieroglyphic records dating back several hundred years BC describe the growing of plants in water, without soil. Before the time of Aristotle, Theophrastus (327-287 BC) undertook various experiments in crop nutrition. Botanical studies by Dioscorides date back to the first century A.D.
In the 11th century, The Aztecs of Central America, a nomadic tribe that was driven onto the marshy shore of Lake Tenochtitlan in the central valley of what is now Mexico, practiced hydroponic growing methods out of necessity. Without land to grow plants, they were forced to learn other ways of producing crops. Being a very ingenuous people, they built rafts out of rushes and reeds, lashing the stalks together with roots. They dredged up soil from the shallow bottom of the lake and piled it onto the rafts.
Below are some helpful books on hydroponic growing along with some more history of hydrponics.