Big Hat Logan is a scholar of the soul arts. He is searching for more wisdom in Lordran.
Master Logan was a famous Sorcerer and a royal member of the Vinheim Dragon School before he turned Undead. His nickname stems from the gigantic hat he wore, which completely hid his face. He was hailed as the greatest sorcerer of the Vinheim Dragon School, despite his methods considered to be heretical, as he believed in no gods, no transcendence; only truth.
Logan, as everyone who turned Undead, was exiled and he started his search search for the legendary Regal Archives, which houses the knowledge of the Father of Sorceries. Logan is credited with having developed the Soul Spear Sorcery among others, which is referenced repeatedly in the legends and is said to be on-par with Lord Gwyn's lightning.
In his attempt to reach Anor Londo, presumably to gain access to The Duke's Archives and thus, its vast store of endless knowledge, he became imprisoned in Sen's Fortress, where he first encounters the Chosen Undead. He says he is going mad from the inactivity, and offers to teach the Chosen Undead spells in exchange for releasing him. Upon releasing him, Logan returns to Firelink Shrine to take notes, promising to impart his knowledge to the Chosen Undead when they are next at Firelink Shrine. He doesn't stay long though.
He ventures forth Sen's Fortress and eventually arrives to the Duke's Archives, only to be captured again. Later, if released, he is found studying Seath's books and seems to be losing his sanity.
His final appearance is in the original room where Seath the Scaleless is first encountered. Logan has gone insane and is hostile to the player.