In Star Wars Episode 1, The Phantom Menace, the bad guy for the showdown was Darth Maul, the apprentice of the evil Darth Sidious/Future Emperor Palpatine. In Episode 2, Attack of the Clones, the Bad guy in this is Count Dooku. Played by Christopher Lee, who also played Saruman the White in Lord of the Rings.

The opening titles show that he is the leader of a seperatist group trying to leave the Galactic Senate. His position is so threatening that the senate is seriously considering raising an Army of the Republic to guard against the threat of the Seperatists. Such an action might only invite war. From there the movie begins.

From some of the Dialogue, and if you read The Expanded Star Wars Universe, you can find more about him. He was Yoda's apprentice, and became a very powerful Jedi.

From Starwars.com:

Count Dooku was once a revered Jedi Master whose personal beliefs often clashed with that of the Jedi Council. He believed that the Jedi should not serve so corrupt an institute as the Republic, and 10 years ago, he turned his back on the order, becoming one of the few Jedi to voluntarily renounce his commission. Dooku resurfaced years later as the head of the Separatist movement. His powerful presence and charismatic demeanor have swayed thousands of systems to abandon the Republic in favor of reform.

Qui-Gon Jinn was his apprentice, who apprenticed Obi-Wan Kenobi, who in turn led to Anakin Skywalker/Darth Vader.

From here on it's a Spoiler: He's busy with the trade federation building a robot army to break away, a treasonous act.

Near the end of Attack of the Clones, he retreats, taking the plans for the Death Star to the Emperor. Obi-Wan and Anakin try to stop him, but Dooku uses the power of the Dark side and the Force to hurl bolts of energy at them. There is a lightsaber battle and Anakin gets his arm cut off. Dooku is so corrupted by the Dark Side that he claims "I am the most powerful Jedi ever!" Perhaps Anakin is heading down that path too.

Yoda enters. It's a major showdown, Master versus apprentice. Good versus Evil. Since the same actor from Lord of the Rings does battle again with his powers, many people compare the battles, Saruman vs Gandalf, Dooku vs Yoda. This fight is much better. See the writeup on Yoda for the full description.

Now Dooku is called Darth Tyranus, as he's the apprentice of the Evil emperor Darth Sidious, who helps turn his power towards evil.

Thanks to anotherone, shro0m and Jpers36 for the corrections

Darth Tyrannus led the Confederacy at the Battle of Coruscant during the Clone Wars. However, the fallen Jedi, well-known for his intelligence, class, wealth, and sheer power, would suffer an embarrassing and crushing defeat at the hands of General Obi-Wan Kenobi's Grand Army of the Republic.

Kenobi's daring plan to rescue the Supreme Chancellor Palpatine was a success; however, Kenobi was unaware that Palpatine was pulling the strings behind his own kidnapping and that he was behind the machinations of the Grand Army as well as the Confederate Army. The Battle of Coruscant was really a trap designed by the Chancellor to see if the Chosen One Anakin Skywalker could be turned to the Dark Side. Count Dooku was privy to his master's plans, with the exception that he realized only too late that Palpatine was permanently replacing him. Palpatine had promised Dooku that if Anakin gained the upper hand, he would join the fight. He was lying however. He was just using Dooku, and Dooku learned only too late the Sith's nature of turning against each other. Dooku, also known as Darth Tyrannus, was a great warrior but he had the supremely bad luck of going against the Chosen One, Anakin Skywalker, potentially the most powerful Jedi or Sith of all time, just as Anakin was hitting his prime.

Tyranus himself was executed in one on one combat by the legendary Jedi Knight, who would eventually succeed him as Dark Lord of the Sith. Tyranus was also succeeded by General Grievous in his position as leader of the Confederacy. However, the Confederacy was never able to recover from Dooku's death, and the Republic won the Clone Wars. The "victory" was a pyrrhic one though because the head of the Republic, Palpatine, was also a Sith Lord. The Republic was quickly reorganized as the Galactic Empire after the War.

In fairness to Dooku, he should probably be considered one of the top 10 Jedi as well as top 10 Sith Lords of all-time. He completely demolished Kenobi in personal combat in both his confrontations with him. He also went toe to toe with his old master Yoda and held his ground before deciding to run away. Had he been a little more ambitious he might have recruited Anakin himself and overthrown Darth Sidious/Chancellor Palpatine, thus allowing himself the freedom to implement his own visions for the Jedi Council and Galactic Republic, two institutions which he obviously was gravely intent on reforming. Why else would he have conspired with Palpatine to start the Clone Wars? So close but no cigar. His perverted idealism was ultimately betrayed by the selfish ambition of Palpatine.

Dooku converted to the Dark Side soon after the Death of Darth Maul at the Battle of Naboo. He may have been disillusioned by the death of his apprentice Qui-Gon Jinn (who in turn was Kenobi's master), a death which he apparently blamed on the Jedi Council.

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