These volumes will be essential references for research and postgraduate mathematicians whose work involves group theory.These volumes contain selected papers presented at the international conference on group theory held in St Andrews in 1989. The themes of the conference were combinatorial and computational group theory; four leading group theorists (J. A. Green, N. D. Gupta, O. H. Kegel and J. G. Thompson) gave courses whose content is reproduced here.These volumes contain selected papers presented at the international conference on group theory held in St Andrews in 1989. The themes of the conference were combinatorial and computational group theory; four leading group theorists (J. A. Green, N. D. Gupta, O. H. Kegel and J. G. Thompson) gave courses whose content is reproduced here.These two volumes contain selected papers presented at the international conference on group theory held at St. Andrews in 1989. The themes of the conference were combinatorial and computational group theory; leading group theorists, including J.A. Green, N.D. Gupta, O.H. Kegel and J.G. Thompson, gave courses whose content is reproduced here. Also included are refereed papers presented at the meeting.Introduction; 17. A survey of recent results on projective representations of the symmetric groups J. F. Humphreys; 18. Some applications of group theory in combinatorial group theory A. Ivanov and A. Yu. Ol'Shanskii; 19. Rational growth of wreath products D. L. Johnson; 20. The modular group and generalized Farey graphs G. A. Jones, D. Singerman and K. Wicks; 21. On the n-centre of a group L. C. Kappe and M. L. Newell; 22. Existentially closed finitary linear groups O. H. Kegel and D. Schmidt; 23. Permutability and subnormality of subgroups R. R. Maier; 24. Some applications of powerful p-groups A. Mann; 25. Combinatorial aspects of finitely generated virtually free groups T. M?ller; 26. Problems in loop theory for group theorists M. Niemenmaa; 27. Sylow theory of CC-groups - a surveyl#)