The aim of the paper under review is to construct new solutions to the quantum Yang-Baxter equation. The well-known construction of \textit{V. G. Drinfeld} is to quantize the solution to the classical Yang-Baxter equation resulting from a Manin triple [Proc. Int. Congr. Math., Berkeley/Calif. 1986, Vol. 1, 798-820 (1987; Zbl 0667.16003)] to obtain solutions of the quantum Yang-Baxter equation. In the paper under review, the author introduces the notion of associative Manin triples which consist of a symmetric algebra (that is an associative algebra equipped with a symmetric, cyclic, non-degenerate pairing) and a pair of subalgebras satisfying certain conditions. The examples of solutions obtained by this method also satisfy the Hecke equation, and thus, in a sense, solutions of type \(A\). It is not known whether one can obtain solutions of other types.