The character Angel/Angelus is played by David Boreanaz, known affectionately in the fandom as DB
Name: Angel, Angelus, Liam
Giles: Not long for a vampire. Uh, two hundred and forty years or so.
Buffy: Huh! Two hundred and forty. Well, he said he was older.
Giles: (sits and looks through the diary) Angelus leaves Ireland, uh, wreaks havoc in, in Europe for, uh, several decades, and then, um, about eighty years ago, the most curious thing happens. He, he comes to, uh, to America, um, shuns other vampires, and, and lives alone. There's, there's no, no record of him hunting here.
Buffy: I invited you into my home and then you attacked my family!
Why not? I killed mine. I killed their friends... and their friend's
children... For a hundred years I offered ugly death to
Buffy: What changed?
Angel: Fed on a girl about your age... beautiful... dumb as a post... but a favorite among her clan.
Buffy: Her clan?
Angel: Romany. Gypsies. The elders conjured the perfect punishment for me. They restored my soul.
Buffy: What, they were all out of boils and blinding torment?
Angel: When you become a vampire the demon takes your body, but it doesn't get your soul. That's gone! No conscience, no remorse... It's an easy way to live. You have no idea what it's like to have done the things I've done... and to care. I haven't fed on a living human being since that day.
In Passion, Angelus sketches Buffy while she’s sleeping and her mother while she’s sleeping as well. This artistic flair is carried over into later episodes and AtS.
First Appearance in Welcome to the Hellmouth, Season 1, Episode One.
Angel already knew who she was before he met her (WttH). He follows her on her way to The Bronze and he gives her a cross as a gift and informs her that The Harvest is coming and that they are standing at the mouth of Hell.
In Bewitched, Bothered and Bewildered, he gives Drusilla the still warm heart of a "quaint little shopgirl." He also sends Buffy a dozen red roses along with a card bearing a single word: Soon.
Angel does not appear in The Puppet Show or Nightmares or Inca Mummy Girl,
Buffy first calls the vamp face "Game face" in Prophecy Girl
Buffy sends Angel to hell to stop Acathala from sucking the whole world there in Becoming II.
Angel comes back from Hell at the end of Faith, Hope & Trick, after Buffy goes there and leaves her Claddaugh Ring on the floor of the mansion. Angel falls from the sky in a bright light and lands exactly where she left the ring.