This is a post i did a while ago which may be of some use here.
Ancient Egypt is considered to be the motherland of alchemy. The source of chemistry is also considered to be the Alexandrian academy that was founded by Alexander the Great in 332BC. The new capital city of Egypt Alexandria became the centre of alchemy and other sciences.
Greeks brought their natural philosophy and the works of Plato and Aristotle to Egypt and chemistry was developed allot. The Alexandrian academy was the place where practical chemistry was combined with the theory of ancient Greece and became the place of birth of the science that people called Khemia (transmuting metals)
The Christianity establishment as the main culture of the Roman Empire led to the damage of alchemy, its followers were caught and executed. As the centre of alchemy was the Alexandrian academy there were many attempts to ruin it by Christians. Officially the Alexandrian academy stopped its existence after Egypt was conquered by Arabs in 640
Basically speaking alchemy is the study of the elements fire, water, earth and air, and the study of transmutation. The people who studied this were called Alchemists.
In Medieval times it was studied to learn how to change lead into gold. Similar to chemistry but as we know much older. Alchemists also tried to make the elixir of life which would give immortality. Many times alchemists would use stories and legends to try to veil and prove their theories on how to make gold.
Alchemy is not a science as such, but the theories alchemists had were important for other sciences like chemistry. There is also a link with alchemy and psychology. While alchemy deals with the external existence and psychologists deal with the inner life of man. The saying As above down bellow is used to veil the relationship existing between alchemy and psychology.
The myth of alchemy is the philosophers stone, which was an alchemical substance capable of turning base (impure) metals in to pure gold. In reality the closest we have come to this was in 1980, when a scientist changed a small amount of bismuth in to gold with a nuclear reactor. But the cost to do it was more than the gold was worth.
The main reason alchemy is important is it helped the sciences that came after it, physics, biology, chemistry and astronomy. Alchemists were basically philosophers / scientists but they did seek enlightenment.
I suppose you could call alchemy Magical chemistry, as it combines the usual with the unusual, claiming that magic can be achieved through the law of physics.
Today this science is considered to be dead. Moreover it is now no longer considered a science at all. Modern scientists believe alchemy is just the ancient ancestor of chemistry.