Asymptotic Combinatorics with Applications to Mathematical Physics : A European Mathematical Summer School held at the Euler Institute St. Petersburg Russia July 9–20 2001 At the Summer School Saint Petersburg 2001 the main lecture courses bore on recent progress in asymptotic representation theory: those written up for this volume deal with the theory of representations of infinite symmetric groups and groups of infinite matrices over finite fields; Riemann Hilbert problem techniques applied to the study of spectra of random matrices and asymptotics of Young diagrams with Plancherel measure; the corresponding central limit theorems; the combinatorics of modular curves and random trees with application to QFT; free probability and random matrices and Hecke algebras