This volume constitutes the proceedings of the 3rd Symposium on Stochastic Algorithms, Foundations and Applications (SAGA 2005), held in Moscow, R- sia, at Moscow State University on October 20-22, 2005. The symposium was organized by the Department of Discrete Mathematics, Faculty of Mechanics and Mathematics of Moscow State University and was partially supported by the Russian Foundation for Basic Research under Project No. 05-01-10140-?. The SAGA symposium series is a biennial meeting which started in 2001 in Berlin, Germany(LNCS vol. 2264). The second symposium was held in Sept- ber 2003 at the University of Hertfordshire, Hat?eld, UK (LNCS vol. 2827). Sincethe?rstsymposiuminBerlinin2001,anincreasedinterestintheSAGA series can be noticed. For SAGA 2005, we received submissions from China, the European Union, Iran, Japan, Korea, Russia, SAR Hong Kong, Taiwan, and USA, fromwhich 14 papers were?nally selected for publication after a thorough reviewing process. The contributed papers included in this volume cover both theoretical as well as applied aspects of stochastic computations, which is one of the main aims of the SAGA series. Furthermore, ?ve invited lectures were delivered at SAGA 2005: The talk by Alexander A. Sapozhenko (Moscow State University) summarizes results on the container method, a technique that is used to solve enumeration problems for various combinatorial structures and which has - merous applications in the design andanalysisof stochasticalgorithms. Christos D. Zaroliagis (University of Patras) presented recent advances in multiobjective optimization.