In American English, a "formal" is organized by a college or university organization, typically but not always a fraternity or sorority.

formal power series, a generalization of power series without requiring convergence, used in combinatorics;

In Australian or British English, a "formal" is the equivalent of the American prom dance.

short or prefix form for formaldehyde

formal set theory as opposed to naive set theory;

formal language, comprising the symbolic "words" or "sentences" of a formal system;

formal grammar, a grammar describing a formal language;

Informal economy

formal methods in computer science, including:

formal verification proves correctness of a system

formal system, an abstract means of generating inferences in a formal language;

relating to form, i.e. appearance rather than essence.

relating to Formalism, i.e. emphasis on form over content or meaning.

Formal occasion

Formal attire worn on such occasions

formal derivative, an operation on elements of a polynomial ring which mimics the form of the derivative from calculus.

Formal equivalence word-for-word translation (especially of the Bible)

Formals are particular meals at some British universities

formal calculation, a calculation which is systematic, but without a rigorous justification;

formal specification describes what a system should do, not how it should do it

Formal cause, Aristotle's intrinsic, determining cause.

synonym for dimethoxymethane

relating to formality

Informal occasion (included as Informal redirect here); see Dress code (Western) for the distinctions between Formal, Semi-formal, and Informal

Informal attire (not to be confused with Casual -- see Dress code (Western))