The Old Republic

The Republic began millenia ago. Made of many worlds and species, joined together in a democracy to promote peace and free trade. It came together along established hyperspace trade routes with it's center on Coruscant.
Representation Each system has representative sent to the Senate, where, ideally, they debate and act for the common good. But good intentions are not always enough. Sometimes corruption leaks in. Other times the best interest of one world isn't so good for another.
Beliefs:
The Republic Beliefs: Slavery is illegal, the rights of all sentients must be respected and the sovereignity of a world or system must also be respected. Within these guidelines, individual planets choose their own laws.
The judicial system allows for claims of violation of rights and prosecutes crimes that cross the planetary systems, such as piracy.
Jedi Mediation The golden age of the Republic was guaranteed in part by the Jedi. Their force powers, mandate to serve, and mediation combined with battle skills enabled them to challenge galactic criminals and ferret out the truth between conflicting governments, working to negotiate peaceful compromise.
End:
The end of the Republic was also the end of the Jedi. Working from within the Sith Darth Sidious, who most knew as Senator Palpatine, became Supreme Chancellor.
Working from within the Senate itself, he manipulated governments, pretending friendship with their senators while secretly turning them against each other and the Republic.
His apprentice Darth Tyrannus, also known as Count Dooku, created the Separatists. The Clone Wars, ensued.Palpatine was given emergancy powers. Rights were 'temporarily' overridden in the name of security. While the Republic Senate believed they fought the Separatists, the Jedi took on roles of generals.
The war seemed almost won. After supposedly taking the Supreme Chancellor hostage, Dooku was killed by Anakin Skywalker. A lead opened up on his chief enforcer General Grievous. Then, Palpatine made his move. He tricked the Jedi into sending Obi-Wan Kenobi after Grievous, leaving Anakin without his guidance to counter Palpatine's emotional attack.
He used Anakin's divided personal loyalties - his forbidden love for Padme, and the friendship he'd cultivated since Anakin was just a boy - against him.
He lured him to the Dark Side with the promise of the power to save people, including his wife, from dying. The price: destruction of the jedi.
Anakin became Darth Vader and obeyed the order to invade the jedi temple and slaughter them all. Those not at the temple were in the battlefield, surrounded by troops ordered to kill them.
In the end, he used the very armies they led to destroy them, claiming a Jedi Rebellion against the government. The Republic died to the cheers of the Senators as he reformed it into an Empire.
The Empire
The Empire's formation began on the blood of innocents, the jedi who had so valiently served the Republic. Villified, the were forced into hiding. Meanwhile the rights of the people were rapidly being diminished, with more and more power given to Palpatine. Finally, in secret, some Senators joined together in forming an Alliance to Restore the Republic. Those instrumental were Bail Organa, Mon Mothma and Garm Bel Iblis.
Beliefs:
Divide and conquer. The Empire persecuted all non human species. Not coincidentally, the most prominent members of the former separatists were non humans. Woman also saw a great deal of discrimination.
End of Power:
This Rebel Alliance began with limited resources. Garm Bel Iblis vanished after an assassination attempt and a falling out with Mon Mothma. But the biggest spike in Rebel support came with the Death Star. The Empire used their new super weapon, with the planet Alderaan as an example. The entire planet was destroyed, along with Bail Organa. Survivors of Alderaan flocked to the Alliance. Meantime, a young farm boy from Tatooine, Luke Skywalker, was sucked into the alliance by a message from Princess Leia Organa and the jedi master Obi-Wan Kenobi. With a single shot and some cover fire from his smuggler friend Han Solo, he destroyed the station.
Rebel Allies: Republic Allies included the Bothan's who spynet was legendary and the Mon Calamari, whose ship building skills were to become a powerful component of the Alliance Fleet.
The downfall of the Empire was due, in part, due to the combined efforts of the Jedi and the Alliance. With Luke Skywalker now the last of the Jedi and a member of the Alliance, Palpatine set a trap for the alliance fleet. The bait: himself and a new Death Star. When the Alliance team approached to sabotage the shield for the unfinished station, Luke sensed Darth Vader. Both to divert him from the team and to confront him, he surrendered. The Alliance team along with the native allies, succeeded in destroying the shield. Luke battled Vader and the Emperor and succeeded not only in defeating Vader in combat but in winning him back to the Light. He turned on the Emperor, sacrificing his own life to save his son. Thus, the Emperor was destroyed. The Empire, however, continued the war with the Rebel Alliance, refusing to accept the 'New Republic' it became. It was twenty years before a peace treaty was signed.

The New Republic
Beliefs:
The same as the Old Republic. Freedom, Democracy, with a system that struggles to balance individual sentient rights, planet rights, and need for an intergalactic government.
A New Beginning. With the Emperor's Death and his main fleet scattered after the battle of Endor, the Alliance sent out emissaries to the galaxy, inviting them to help form the New Republic. Some worlds had representatives even while still oppressed by the Empire. While war waged on, diplomacy had now begun. A temporary council was established to govern. Unlike in the Empire, worlds had a choice in whether to join.
The early years The new government faced two huge setbacks. The first was Grand Admiral Thrawn, a military genius whose military prowess reclaimed many worlds. Just as he was killed, a new setback hit. It turned out Darth Sidious had left a Clone of himself behind. War ripped apart the galaxy and the New Republic was forced off Coruscant and back to a military government. However, the Clone Emperor was finally defeated and the war tipped in their favor, allowing for the government to return to a more civilian one on provisional status.
The Next Steps Two major advancements in the government came: first, Luke Skywalker set up his Jedi Academy. While some regarded it with trepidation, his goal was to restore the peacekeepers to the galaxy. The second came when former Imperials were allowed into the Senate. This too was a controversial decision, but also marked a sign of healing in the galaxy.
A New Threat The biggest threat not only to the Republic but the whole galaxy came when an invader from outside the galaxy attacked. Completely unprepared for these invaders unusual organic weapons, the Republic once more was chased off Coruscant. Many Senators were killed. Eventually, with the aid of the Jedi, the war was one and peace reached. But due to appearances, that the Republic had failed twice (first the old, then the new) they renamed it the Galactic Alliance. New leadership had to be elected. This also marked the first coordinated full scale battle effort since the peace treaty was signed between the Empire and the New Republic.