The two-volume set LNCS 8634 and LNCS 8635 includes the peer-reviewed conference proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science, which took place in August 2014 in Budapest, Hungary. These volumes contain 95 revised full texts as well as 6 invited talks, selected from a total of 270 submitted papers. The conference covered a wide range of topics relevant to the mathematical and theoretical foundations of computer science, including logic, semantics, automata theory, programming, algorithms, complexity, parallel and distributed systems, and quantum computing. This collection provides valuable insights and current research findings in these dynamic areas of computer science.