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The Old Republic has four Jedi classes and four Sith classes. These classes are set up like nothing we've seen in an MMO to date. Most massive online games have the same types of class archetypes:
the tank, the healer, and the magic-user. Bioware obviously couldn't walk away from these archetypes completely but neither do any of their classes fit directly into these norms.
The four Jedi classes are the Trooper, the Smuggler, the Jedi Knight and the Jedi Consular. Although each class seems to have tank attributes, the Trooper and Jedi Knight would be the closest to the traditional tank archetype. The Smuggler would be most closely related to a rogue or hunter class. The Jedi Consular is a beast all its own, maybe a distant relative of the Paladin class.
The Sith have their own classes. Unlike other MMOs these classes do not directly mirror their good natured counterparts, although

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there are similarities. The Sith are comprised of the Bounty Hunter, the Imperial Agent, The Sith Warrior and the Sith Inquisitor.
Each class, both light and dark, has its own story line that will be followed as you level your way through the game. Each choice made while questing will shape your character and determine what skills they will gain.