David Boreanaz as Angel

I am not a drooling Angel fan. I think he has a nice body and an attractive face, but he is not my favourite man on the show (that would have to be Spike, closely followed by Xander). What I like best about Angel is his role in the Big Picture. I find Angelus a much more interesting character than Angel, but I find that either way, Angel(us) adds an interesting dimension to the cast of Buffy. As Angel he is tormented by guilt, as Angelus he is brutal and remorseless, yet in both states he is obsessed with Buffy. It's been very exciting to see Angelus in action this season; it's made for some great Buffy angst, it's kept things from getting too pedestrian (a happy couple may be sweet, but they don't make for the most interesting storylines), and it's allowed for some amazing plot developments (ie character death, tough decisions, etc.). I can't wait to see what he'll do next.

Angel is a Vampire who is about 240 year old. He is unique among Vampires for one very crucial reason: he has a soul. When a person is turned into a Vampire they lose their soul, and this happened to Angel. Things changed when he killed a Gypsy girl who was favoured among her tribe. The Gypsies wanted revenge, and so they put a curse on Angel, giving him back his soul and condeming him to an immortal lifetime of guilt. And he was miserable, until Buffy came into his life. Angel was determined to help Buffy in her destined role, and provided her and her Watcher with crucial information when she first arrived in Sunnydale. But his role as "Mr. Cryptic Message Guy" didn't stay so simple for long. He fell in love with Buffy, admiring her strength, bravery, beauty and pretty much everything else about her.  And she fell in love with him. The two tried to stay apart, but their feelings were too intense. They made love on Buffy's seventeenth birthday.

Angelus

Angelus is Angel when the demon is in control. Angelus is a brutal killer (he kills with a song in his heart) and has a tendency to fixate on young women. He fixated on Drusilla during his first stint as a Vampire, and after driving her insane by killing her family and friends (and leaving little gifts like a dead puppy nailed to her door), he converted her into a Vampire on the night she was to take her holy vows at the convent she had fled to. Angelus was suppressed and Angel took control during the 90 years of the curse, but that curse was broken when Angel slept with Buffy (the intent of the curse was to punish Angel, and thus if he experienced a moment of happiness, it would be destroyed and the demon would regain control). Now Angelus is back in control, and he has fixated on Buffy. Repulsed by the love his human self felt for her, he is determined to drive her mad as well, and has begun torturing her by killing her friends and reminding her of her love for Angel.

Episodes Featuring Angel/Angelus
Giles is a regular character, and as such is in every episode. Listed below are episodes which feature his character specifically, or in which significant character development occurs.
(All transcripts generously provided by AleXander)

Season One
1. Angel: When Angel helps Buffy when she is attacked by powerful Vampires known as The Three, she brings him back to her house to bandage him up. The two become close, but she learns something about him that will change their relationship forever. Is he a friend, or has he simply been trying to deceive her into trusting him?

Season Two
1. What's My Line, Pt. 2: Spike and Drusilla's plan to restore Dru's strength requires the blood of her sire: Angel. If the ritual works, Angel will die. And he will, unless Buffy and company make it there in time.
2. Surprise: Buffy's birthday surprise takes a sad turn when Angel must prepare to leave Sunnydale for years to take a piece of a disassembled demon to the ends of the Earth. After sharing a dangerous moment, Buffy and Angel make love for the first time. Later, in Innocence, Angel awakens without his soul, and joins forces with Spike and Drusilla as Angelus.
3. Passion: Angelus ups the stakes on his torment of Buffy by harassing her friends (whose houses he has been invited to enter as Angelus), watching her sleep, and even killing someone close to her.
4. I Only Have Eyes For You: Buffy begins to forgive herself for Angel's transformation when she and Angel are possessed by the ghosts of a teacher and student who were having an affair and died in a murder/suicide 43 years ago.