This volume contains the invited lectures of a school on modern quantum field theory held at Alushta, USSR, in May 1989. The development of this subject, including string theories attempting to model elementary particles, is closely interwoven with modern mathematical physics. The lectures presented by experts in the field provide an overview of the research pursued in different branches of this rapidly evolving field and draw attention to particular interconnections and problems. Topics covered include: geometrical quantization and finite size effects in conformal field theory; quasi-Hopf, Kac-Moody current and Lie super-algebras; quantum groups; Wess-Zumino-Witten models; Nizhnik-Zamolodchikov equations; non-archimedian strings; string dynamics; KdV and KP (super) equations and calculations on (super-) riemannian surfaces; 2d Ising model and 2d electron motion on surfaces in external magnetic fields.