The modern-day character whose memories are explored in the original Assassin's Creed game is Desmond Miles. Abstergo Industries uses the Animus to access Desmond's genetic memories of his ancestor Altaïr Ibn-La'Ahad.
Desmond is initially held against his will and made to relive Altaïr's experiences. The process allows Abstergo to search for information hidden in the past, while Desmond gradually notices unusual effects and learns that the experiment has a larger conflict behind it.
William Miles is Desmond's father and a later Brotherhood leader, while Warren Vidic is the Abstergo scientist supervising the Animus project. Clay Kaczmarek, also known as Subject 16, is another important Animus subject introduced in the broader series but is not the original game's central modern-day character.