The course "Gauge Field Theory" aims to study both some general methods of field theory and their applications in high-energy physics and condensed matter physics. The presentation is based on the principle of gauge invariance. Abelian and non-Abelian gauge fields are widely used in modern theoretical physics, in particular in the theory of elementary interactions, where the Standard Model is built on their basis. The course aims to introduce students to the principle of constructing gauge models of field theory and to the features of the canonical formalism in gauge field theory. It examines in detail the electroweak sector of the Standard Model, briefly touches on the description of strong interactions and the issue of describing neutrinos. It also examines the application of high-energy physics methods in condensed matter physics.