At its core, alchemy is the search for the divine. Alchemists set out to find mystical substances that give mere mortals a connection to god. They aim to purify objects and themselves, in an effort to interact with heaven. Not only do they want to find and create mystical artifacts, alchemists also utilize what they have and what artifacts they can in their search.
The philosophers stone was the fabled prime matter that was the ultimate secret of almost all European alchemists. This "stone" was said to be the key ingredient to any alchemical experiment. A catalyst for turning base metals into gold ,or even silver. At the time, little was known about elements and material so alchemists had to make assumptions and try and learn about substances through their work. With this in consideration, base elements in alchemy are defined as rare, refined, solid elements that over time, evolve to rarer states. For most substances, this meant they would eventually turn into gold. Alchemists wanted to learn how these elements evolved so that they could speed up the process and replicate the results. The philosophers stone was a substance that was supposed to aid them in this. One problem with the stone is that there is no one, clear way it is depicted. To some it was a literal stone or gem, others thought of it as an elixir, a powder, or even a chalice. With the idea of the chalice in mind, numerous alchemists believed that the stone might be the holy grail depicted in arthurian literature. The philosopher's stone also had many meanings to it. Its most physical properties were its abilities of transmutation. Legends also said though, that if it were to be ground up and taken, it would cleanse the body of impurities, perfect and heal your soul, and extend your longevity. It produced the elixir of life. Another myth that went along with the search for the stone was that you could make yourself, into the philosopher's stone. That through balancing and perfecting yourself, you would discover a new way of existing and seeing connections in the world. It was said that if the stone did exist, one would be changed by the quest more than the discovery.
This image depicts a common symbol for the creation of the philosophers stone called "squaring the circle" which ironically relates to a math equation that, in the mid 1800's was discovered to be impossible.
The elixir of life is another one of the primary goals in alchemy. It was said to be "that which was present at creation", the quintessence. Alchemists wanted to speed god's work and the natural processes to replicate what god did during creation. The elixir was supposed to be a substance that would, at least, grant longevity and better health of, at most, grand immortality and perfect one's body, spirit and soul. Some alchemists believed that the way to find the elixir was through distillation of substances. Others thought the opposite and attempted combining substance's in their search. The elixir of life tied back very heavily to the christian religion and the tale of Adam and Eve. The legend goes that Adam and Eve were in the garden of Eden surrounded by trees that would bring them knowledge. They were told they could eat from any tree except the tree of good and evil. Satan appeared and tricked them into doing so. They were expelled from the garden before they could eat from the tree of life. This is why humans are mortal. At a later time Adam calls to the angels and they give him the knowledge to heal himself. Alchemists believed that this knowledge came from the tree of life and was lost. Through their spells and experiments, they attempted to find it in nature. These religious ideas are very present throughout alchemical work and it has even been proposed that Jesus was an alchemist that fulfilled his objectives.
Magnum Opus or "The Great Work" is basically, the accumulation of what an alchemist does and has done, on their journey to find the philosopher's stone or the elixir of life. On a spiritual level, it was a magical process of refining one's self. Hermetic people (people who believed in the spiritual aspects of alchemy and Hermeticism) saw that the Magnum Opus lead to god and was the transformation from a basic, animalistic human into something pure. They believed that humans were once pure and tried to get back to that state. Alchemists thought that god wanted them to become like him and through redemptive acts, they could reach "apotheosis", the final stage in their development. The mark of a truly good alchemist was that they had completed the great work on themselves.
It has been mentioned repeatedly how secretive alchemists were with their work. Most of their work is written in code or cryptic allegory. There are quite a few reasons as to why this might be. On a philosophical level, some alchemists believed they were chosen by god to do their work and that they had to hide it from those who were unworthy. They wrote cryptically so that only they would know what it meant and so future alchemist, if they be worthy, could understand it. Remember though, at the time when alchemy was around, magic was often seen as taboo and was outlawed by the church. For alchemists, it was very practical to hides their work so as to not be found out and prosecuted. Lastly, there is a more psychological reasoning behind the secrecy. Greed. Alchemist believed they were "chosen" by god and had bought into the philosophy for, quite often, many years. They also see that if they can find a way to turn something into gold, why would they share when they, and they alone, could prosper from these riches. So despite all the religious mumbo jumbo and the duty they felt, it could have truly been greed that gave us alchemy.
Unlike the philosophers stone, the holy grail, or the elixir of life, there is evidence that the emerald tablet truly did exist. There are many rumors and legends that go along with the emerald tablet. One source states that there are 15 tablets written by Thoth (the atlantean priest). These are said to have been found in the early 1900's and translated by a Dr. Doreal placed back in the pyramids. They were indestructible and made from alchemical transmutation. The other tale has only one tablet and is what most alchemists based their work on. It was one of the first texts ever to be translated into Latin and is believed that this tablet was written by Hermes Trismegistus. It is said to hold the secret to alchemy but, it is written in allegory. Many people have attempted to translate it, from Isaac Newton to Albert the Great. The only constant is that which appears on the first lines of the tablet. "As above, and so below". These five word though, have had many a translation and have taken alchemists years to decipher. Albert the Great believed it was how the seven planets correlated to the seven metals. Another interpretation is that it relates to the christian story of Genesis or even is a pre-christian creation myth. Does it represent the relationship between material and spiritual existence? Form and matter? no one really knows. It is one of history's greatest mysteries and yet, one of the things at alchemists core.
The Image on the right is recreation of what they were believed to look like and the one on the left is an illustration of how they could have appeared.
The left link provides 12 translations and a brief summary of the meaning of the tablets. Additionally, it gives interpretations on the meaning of the tablet. The right link is Dr. Doreals translation of the emerald tablets reportedly found in Egypt during WW1.