This volume is the compilation of invited lectures presented at the Spring School Problems of Modern Quantum Field Theory held in Alushta (USSR) April 24-May 5 1989, organized by the Institute for Theoretical Physics (Kiev) and Landau Institute for Theoretical Physics (Moscow). Approximately one hundred physicists and mathematicians attended lectures on aspects of mod- ern quantum field theory: Conformal Field Theory, Geometrical Quantization, Quantum Groups and Knizhnik-Zamolodchikov Equations, Non-Archimedian Strings, Calculations on Riemannian Surfaces. A number of experts active in...