The Library is an interdimensional space where magical mysteries in books and artifacts of a magical nature are cataloged in order to keep them from falling into the wrong hands. Apparently, it is a bad thing if too much true magic is out there free in the world for people to us, at least according to the Library. The Library is sentient and chooses its own staff. There has always been a single Librarian chosen from among many candidates. Most of the time, the Librarian has a Guardian, also appointed by the Library, but this is not as required. Flynn Carsen, current Librarian, as of the time of the series start is very adamant that he does not want a new Guardian when the Library chooses Eve Baird, a colonel in the NATO Counterterrorism Unit, for the job.
The two quickly learn that this is not the only problem at hand, as they realize that someone is killing other highly-qualified Librarian candidates that the Library turned down when it chose Flynn. One of them had almost made it to Flynn to warn him of an impending disaster when he was stabbed to death in broad daylight. They learn that there is a painting of King Arthur and his knights in a museum in Munich and that something about it was apparently so important that this man died trying to tell Flynn. They also realize that the three highly-qualified candidates who failed to show up for their interviews are still alive, so they set off to find them and rescue them from their would-be assassinations.
Some stuff happens, and the primary antagonist organization that comes back now and again, the Serpent Brotherhood, reveals their plan to return a surplus of magic to the would through the leylines. They will do this by returning Excalibur to the stone from whence King Arthur pulled his sword, and so on. Wrong sword for us, but what can you say. Spoiler alert within the spoiler alert: They succeed in returning magic to the world, but do not fully succeed in the rest of their plan. As a result of this and some other events that transpire in the first episode(s), Flynn decides to keep the three Librarian candidates on as Librarians-in-Training while he goes off in search of the rest of the Library.
The show's primary characters are: Eve Baird, mentioned above as a NATO counter-terrorism officer and brand new Guardian, Cassandra Cillian, a synaesthete with a terminal brain tumor which allows her to be exceptionally good at math, Ezekiel Jones, a very young, world-class thief, and Jake Stone, an art history expert who has been voluntarily stranded in his hometown in Oklahoma all his life, hiding his interests and gifts from his friends and family to keep them believing that he is a typical roughneck. And last but not least, there is the man whom I chose the subpar promo picture for: Jenkins, who has another identity, but it's a major spoiler type thing, so let's suffice to say that he is the best grumpy old man you'll ever see.