Alchemy was far more abundant in terms of books thanks to Nicolas Flammels favoritism but was a confusing subject to say the least. There was actually a few schools of thought involved in the subject that all alchemy fell under. The first was transmutation or the changing of one thing into an other permanently. This was accomplished in a few different ways but the final result always requires the alchemist to exchange something of equal worth for the change. Usually this is in the form of mana but it was possible to substitute other things.-
The second school of thought was the displacement school that sought to give magical abilities to an object that the object normally wouldn't have. Things got weird at this point as you could in theory give even a simple pebble the ability to kill a god if you were able to trade the price required for it. Alchemy worked based on the principle of equivalent exchange after all however so the price of such a thing was horribly high. This school of alchemy though had heavy use of ritual circles and heavy material costs that changed in a way that left the alchemist needing to set up the magic from scratch every single time.-
The second to last school of alchemy was the life school and was were things got very messy and dark very fast. The ultimate goal of this school was to create the supreme creature that was perfect in every way. Almost every alchemist in this school was a vile dark wizard or witch as the easiest way to conduct experiments in this school was on living or unborn creatures by fusing external pieces onto them or altering them before birth. This was how an extremely large amount of monstrous magical creatures came about and as such was almost outright banned globally.-
Nick copied the information on the subject but knew he was very unlikely to ever use it. The final school of alchemy was the emotion or soul school and focused on giving emotions or true souls to their creations. This school was the most esoteric of all the schools as it was so difficult to progress in that not even Nicolas Flammel wrote much on it beyond the barest hint of the starting point. This starting point was creating enchantments via ones own emotions to fulfill a need which was extremely powerful magic considering the protection granted to Harry from his mother fell into this school.-
It was thanks to all this information on alchemy that Nick could roughly figure out how Nicolas Flammel managed to create the philosophers stone. See the great alchemist was born just before the black plague ran rampant across Europe and while he may not have created the disease he probably used the lifeforce and deaths of the victims to create the stone as that would be the only way it could allow it to do what it does.-
It explained why no one else had managed to create a stone in this long period of time since that point. Flammel had likely marked the disease so that each of it's victims fueled his alchemical construct at the moment of their deaths. As more and more lives were lost the stone gained greater and greater power until the disease finally was stomped out. By that point though the stone had the sacrificed power of between fifty to seventy five MILLION people killed by the disease. So much power was still not enough to give immortality via life extension but it certainly gave a VERY large increase of maybe a few thousand years.-
It was likely what the "elixir of life" actually was was pure lifeforce distilled into liquid form that likely removed the effects of aging or injury on the body. Nick didn't think any lower of the great alchemist despite figuring it out as what he did while certainly not righteous was also not evil , merely opportunistic. More than likely the way Flammel saw it was that since these people were going to die either way he might as well use them for his own benefit.-
While a callus way of looking at it to modern folk it should be pointed out that this was also a time when muggles actively hunted magical folk down. It was already good enough that Flammel hadn't made the disease way worse to squeeze out some extra profit. Still it was getting late and Nick knew he was going to participate in the final stint of the pageant the next day and finished copying the information down before heading for the dining hall. He didn't need to worry about feeding Dusk or Nazgul while he was here as the school had provided food for them generously.