The 34th International Symposium on Mathematical Foundations of Computer Science, MFCS2009,washeld in Novy ' Smokovec,High Tatras(Slovakia)during August 24-28, 2009. This volume contains 7 invited and 56 contributed papers presented at the symposium. The contributed papers were selected by the P- gram Committee out of a total of 148 submissions. MFCS 2009 was organized by the Slovak Society for Computer Science and the Faculty of Mathematics, Physics and Informatics of the Comenius Univ- sity in Bratislava. It wassupported by the EuropeanAssociation for Theoretical Computer Science. We acknowledge with gratitude the support of all these - stitutions. The series of MFCS symposia has a well-established tradition dating back to 1972. The aim is to encourage high-quality research in all branches of th- retical computer science, and to bring together researchers who do not usually meet at specialized conferences. The symposium is organized on a rotating - sis in Poland, Czech Republic, and Slovakia.