ABSTRACT
The theory of commutative Gröbner bases is well known and properly documented in many textbooks, however it exhibits too many lucky coincidences to be fully generalizable to more complex algebraic structures. The goal of this chapter is to present the similar theory of noncommutative Gröbner bases in a way that is amenable to adaptations for other algebraic structures discussed in this book; as the reader will see later, in many ways, noncommutative Gröbner bases are closer to Gröbner bases for operads than to Gröbner bases for commutative associative algebras.
