General Synonyms:
* Freedom
* Independence
* Autonomy
* Emancipation
* Self-determination
* Unrestraint
* License
* Franchise
More Specific Synonyms:
* Political liberty: Democracy, self-governance, suffrage, free speech, free press, right to assembly
* Personal liberty: Free will, autonomy, self-reliance, individual rights
* Economic liberty: Free market, free trade, capitalism, entrepreneurship
* Religious liberty: Religious freedom, freedom of conscience, separation of church and state
The best synonym to use will depend on the context of your writing or conversation. For example, if you're talking about the freedom of speech, "free speech" would be a more precise synonym than "liberty" itself.