Villain vs Antagonist

Long before I started writing anything, I heard the saying that "every good story has a good villain" - or perhaps that should be "...a bad villain"?!  In any case, I took it to heart as I planned my first novel, and this is what I came up with:

The Dark Master, as he is called, who wears a black robe and causes ripples of terror to pass through the idyllic and utopian communities of Atlan, where the heroine and protagonist of my novels resides. 

Although The Dark Master sounds like a Fantasy cliché, I decided early on that he should be a real and complex character, like the others in my story, and not just a "bad guy" for the sake of having a villain.

In the world I've created for Rhuna, my protagonist, the Dark Master has a name like everyone else, and was a normal citizen of a peaceful society.  His name was Gatherer of Sage, and he was a Herbalist who began to dabble a bit too much in Alchemy and other unknown elements.

His quest to achieve things believed to be impossible or unattainable drove him to rebel against the restraints of society and the criticism by his peers, and before long he was no longer a respected Atlan Master wearing the traditional white robe, but rather a dark one to express his defiance:  hence the moniker, "the Dark Master."

At some point I began to think of the difference between a plain, outright villain, and an antagonist, and realized that some of my other characters, who were basically "good guys" were also antagonists because their viewpoint, opinion or actions brought on a conflict, a new situation and consequences that my heroine, the protagonist, had to deal with.

Now that I've decided what motivated The Dark Master to become such, and what still drives him on, he is no longer a faceless, menacing villain, but a formidable personality that can even be respected or understood to a degree. 

What do you as a reader think about a villain/antagonist you can relate to, or who has depths and dimensions like the good-guy characters in the story?