1.being in accord with established forms and conventions and requirements (as e.g. of formal dress);
pay one's formal respects
2.characteristic of or befitting a person in authority;
formal duties
3.(of spoken and written language) adhering to traditional standards of correctness and without casual, contracted, and colloquial forms;
the paper was written in formal English
4.represented in simplified or symbolic form
5.logically deductive;
formal proof
6.refined or imposing in manner or appearance; befitting a royal court;
a courtly gentleman