What are the core beliefs of a libertarian?

Maximal personal liberty

The libertarian believes that the government that governs least, governs best. He believes in maximum personal liberty and minimum government coercion and intrusion in the everyday lives of citizens. The libertarian believes in small government, especially at the federal level, and not getting involved in foreign entanglements. He believes in personal autonomy, both social and economic.

I have also heard this useful description: A libertarian is more liberal than a Liberal on matters of personal liberty, and he is more conservative than a Conservative on matters of economic autonomy.