Gr\"obner-Shirshov Bases for Universal Algebras

Some results were reviewed in Gr\obner-Shirshov bases method for different varieties (categories) of linear (\Omega-) algebras over a field k or a commutative algebra K over k: associative algebras (including group (semigroup) algebras), tensor product of free associative algebras, Lie algebras, dialgebras, pre-Lie (Vinberg right (left) symmetric) algebras, Rota-Baxter algebras, metabelian Lie algebras, L-algebras, semiring algebras, category algebras, etc. There are some applications particularly to new proofs of some known theorems.