A major solved family of cases of Langlands classification using endoscopy.

Develop the geometric formulation of local Langlands over $p$-adic fields and prove its equivalence with the classical representation-theoretic correspondence.

The foundational local correspondence for general linear groups over nonarchimedean local fields.

Establish the full local Langlands correspondence for arbitrary connected reductive groups over local fields, including packet structure, internal parameterization, and endoscopic character relations.