Abstract. We consider monomial orderings specified by matrices of a special form and suggest a new proof of the well-known fact that every monomial ordering can be obtained in this way. The relations between matrices specifying the same ordering are discussed and the canonical form of a monomial matrix is presented. We give some applications of this ordering presentation to Gröbner bases of ideals. We also discuss orderings on differential variables and differential monomials. We prove the property of well-ordering on differential monomials using only two source properties and without any additional conditions.