Li Gan

Li Gan ("Regan" in the Crunchyroll translation of the anime) is the Sage of Miral Lake and a dedicated magic researcher. He first appears to discuss the world's magic laws with Shiroe, and later is invited by the Enchanter to travel north to Susukino with him.

Appearance
With his disheveled robes and enigmatic appearance, Li Gan sometimes appears to be a shady character. Tetora calls him a "skeleton," a name that he does not seem to particularly mind. Like all Elves, he has characteristically pointy ears.

Personality
Li Gan appears to be mysterious and enigmatic when he first introduce himself to Shiroe and Akatsuki. He holds great interest in studying the laws and mysteries of magic, and is excited by the meeting of three different kinds of scholars present (himself, an Adventurer, and a member of the Kunie clan). He is easily excited by the chance at gaining new knowledge no matter how small. He has immense knowledge of the past of Theldesia and is even able to manipulate the technology of the Ancients.

While he is rather competent as a combatant in Lander terms, enough to best a band of middling Lander knights, he is well aware how pitiful his abilities are compared to an adventurers', and has no problem in admitting that his place is not on the battlefield.

Prior to the Catastrophe
A mage of Miral Lake, his interest lies in magical research, especially World Class Magic. His knowledge is vast, as he is one of a few people who recognized that the entire world of Elder Tale had been altered by magic three times in its history. He named this phenomenon the "World Fraction." Even before the Catastrophe, he was among those that suspected that the Adventurers originated in a more technologically-advanced world.

Summer Training arc
During the Round Table Alliance's arrival at the Ancient Palace of Eternal Ice, Li Gan sensed the person he had been looking for, Shiroe, has arrived while inside his private library. Li Gan appeared to Shiroe and Akatsuki through a portal at the balcony, though his entrance made them ready their weapons in self-defense. He then introduced himself to the two Adventurers. They go to Li Gan's library where they discuss the World Fraction and the Spirit Theory.

Return of the Goblin King arc
A month after the Return of the Goblin King event, Li Gan confronts Shiroe and praises him on creating a new kind of magic. When asked how he knew about it, Li Gan admitted seeing the effects of the new magic during the Goblin Conflict.

Gold of the Kunie arc
Li Gan accompanies Shiroe and Naotsugu north to meet with Kinjo, a member of the Kunie clan, to negotiate for a large amount of gold. Despite his enthusiasm over the congregation of three different types of scholars, his hopes are dashed when Kinjo promptly refuses Shiroe's request without much discussion. He then accompanies the two to Susukino, where Shiroe intended to request Silver Sword's cooperation in overcoming a new Raid quest. During this time, Naotsugu and Li Gan wander Susukino in hopes of finding another possible party member. They stumble upon Tetora, who had fallen in the snow, and Li Gan reveals his liking for panties. He casually mocks Tetora's Idol act, much to her displeasure.

After Shiroe and Naotsugu finish their mission, Li Gan decides to stay in Susukino to finish up his research on the Transport Gates.

Homesteading the Noosphere arc
Months later, Li Gan returned to Akiba to share his findings with Shiroe. He discovered that the Transport Gates required large amounts of Mana in order to be powered up and that they are related with the lunar cycle, and the supply of that Mana has somehow been cut off.

Shiroe speculated that there might be ancient Alv ruins on the moon and while Li Gan could not confirm this, he does speak of legends about Alvs having once resided on the moon in ancient times. While discussing methods to establish communications with the Travelers who are based there, it was Li Gan who suggested that he should go to Shibuya, as there is a legend that the old NHK Communications Tower has a method to do just that.

However, before they could establish anything further, a crisis occurred involving hundreds of thousands of Moonlight Moths attacking player cities putting many Landers and Adventurers into a deep sleep, so Shiroe formed the Shibuya Raid Team. Li Gan used this opportunity to join them, first to record this unprecedented event and second to unlock the seal to the dungeon raid zone, which the Communications Tower had become. While being the weakest member on the team and requiring heavy protection, he was able to hold out on his own quite a few times by casting defensive shields against enemy foes.

Collapse of the Round Table arc
Thanks to Li Gan's research on the Transport Gates, Shiroe, to back Rayneshia's faction, restarts Akiba's Transport Gate as a display of power and authority during the vote between her and Eins.

Log Horizon: New Adventure Land
So far, Li Gan has not been made a recruitable character in the SNG, but he appears when you visit the Archives, where you can read past scenarios that you have seen.

Equipment
The headpiece he wears grants him insight and memory retention beyond normal capabilities, and is an item handed down upon Sages of Miral Lake.

Trivia

 * Although volume 7's character page lists his name as "Regan," his name in Japanese is written with a space (the = sign) in the middle, creating "Re Gan." It has also been spelled as リ・ガン, with the interpunct separating the two words.