  The theory of flag algebras, introduced by Razborov in 2007, has opened the
way to a systematic approach to the development of computer-assisted proofs in
extremal combinatorics. It makes it possible to derive bounds for parameters in
extremal combinatorics with the help of a computer, in a semi-automated manner.
This article describes the main points of the theory in a complete way, using
Mantel's theorem as a guiding example.
