Lebensraum (Living Space)
Hitler wanted to claim territory for Germany in the east. This was called "Lebensraum", meaning "living space".
Unite German Speakers
Hitler wanted to unite all German-speaking people. This would mean taking over countries such as Czechoslovakia and Austria, which had many German speakers.
Overturn the Treaty of Versailles
Hitler and many Germans hated the Treaty of Versailles because of its harshness towards Germany after World War I, and the fact that it was a forced treaty ("Diktat"). Hitler promised that he would overturn the TOV, which gained him much support.
Hitler hated Communism. He promised to destroy it once in power.