Short answers, pulled from the story.
The Galactic Empire is the main antagonistic faction of the Star Wars original trilogy, first introduced in the 1977 film Star Wars. It is a fictional autocracy that rules millions of planetary systems through intimidation, coercion, state terrorism, and genocide.
The Galactic Empire rose through the gradual subversion of the Galactic Republic by Supreme Chancellor Palpatine, who used manufactured crises, emergency powers, and a false-flag war to eliminate the Jedi Order and seize absolute rule. He reorganized the Republic into the Empire with himself as Emperor for life, an act the Senate approved overwhelmingly.
Emperor Palpatine rules the Galactic Empire as a Sith Lord, with Darth Vader serving as his second-in-command and Commander-in-Chief. Grand Moff Wilhuff Tarkin, Grand Admiral Thrawn, and Grand Vizier Mas Amedda are among the most prominent senior figures.
The Tarkin Doctrine is the Galactic Empire's core military philosophy, presented by Grand Moff Tarkin to Palpatine in 18 BBY. It holds that rule can be maintained through fear of force rather than force itself, with massive military displays and the Death Star as its ultimate instruments.
The Galactic Empire largely collapses after the Battle of Endor, when Darth Vader kills Palpatine and the Rebels destroy the second Death Star. The Empire is formally defeated about a year later at the Battle of Jakku, leading to the establishment of the New Republic.
Creator George Lucas deliberately modeled the Galactic Empire on Nazi Germany, incorporating uniform designs, a flag resembling the Nazi German flag, and the name of the stormtroopers, which echoes the Sturmabteilung. The political rise of Palpatine also parallels Augustus Caesar's consolidation of power in ancient Rome, and the Emperor's arrival ceremony in Return of the Jedi was inspired by Soviet October Revolution Day military parades.