摘要：Renormalization is usually referred to a process in quantum field theory to extract a finite value with physics meaning from a divergent Feynman integral. This process has been applied by the physicists for several decade with great success, but was described in a mathematical framework only recently through the breakthrough of Connes and Kreimer. Their framework also makes it possible to apply the renormalization method to study divergen cies in mathematics. We will describe the main ingredients  in the Connes-Kreimer framework, including Hopf algebra, Rota-Baxter algebra and algebraic Birkhoff decomposition. We will then apply this framework to study divergent multiple zeta values, which have taken an important place in arithmetic geometry.