In the original Assassin's Creed, the modern-day protagonist who relives Altaïr's memories is Desmond Miles.
Desmond is a descendant of Altaïr Ibn-La'Ahad and is forced by Abstergo Industries to use the Animus, a machine that reads genetic memories. The player experiences the medieval story through Desmond's sessions, although most of the game takes place as Altaïr in the Holy Land.
Desmond escaped the Assassin Brotherhood before the events of the game and lived under an assumed identity. Abstergo abducts him because his ancestry may reveal the location of a Piece of Eden. The company presents the Animus project as historical research, but its leadership has a larger technological and political goal.
William Miles is Desmond's father, while Clay Kaczmarek is another Assassin connected to the Animus project. Warren Vidic is the Abstergo scientist supervising Desmond. These names are sometimes confused because all are important to the modern-day storyline.