【报告摘要】Even though the research style of algebra and analysis are quite different, many algebraic structures naturally arose from analysis, differential equations and integral equations, inspiring further applications in broad areas of mathematics and mathematical physics. Differential algebra is a well-established area from differential equations. This talk gives an introduction of algebraic structures arising from integral operators and integral equations, including Rota-Baxter operators and Reynolds operators. We also give an formal algebraic framework for integral equations.