A Rota-Baxter algebra is an associative algebra together with a linear operator that satisfies an identity abstracted from the integration by part formula in calculus. The study of Rota-Baxter algebra originated from the probability study conducted by Glenn Baxter in 1960, and was developed further by Cartier and the school of Rota during the 1960s and 1970s. Independently, beginning in the 1980s, this structure appeared in the Lie algebra context as the operator form of the classical Yang-Baxter equation. Since the late 1990s, Rota-Baxter algebra has experienced a quite remarkable renascence, leading to important theoretical developments and applications in mathematical physics, operads, number theory, and combinatorics. Most papers on Rota-Baxter algebra have been published during the last ten years.

This monograph is the first on Rota-Baxter algebra written by a leading expert in this fascinating area, introducing the reader to three aspects of Rota-Baxter algebra, and providing plentiful examples and applications, with a complete bibiliography.