On the occasion of the 150th anniversary of Sophus Lie, an International Work­ shop "Modern Group Analysis: advanced analytical and computational methods in mathematical physics" has been organized in Acireale (Catania, Sicily, October 27­ 31, 1992). The Workshop was aimed to enlighten the present state ofthis rapidly expanding branch of applied mathematics. Main topics of the Conference were: . classical Lie groups applied for constructing invariant solutions and conservation laws, . conditional (partial) symmetries, . Backlund transformations, . approximate symmetries, . group analysis of finite-difference equations, . problems of group classification, . software packages in group analysis. The success of the Workshop was due to the participation of many experts in Group Analysis from different countries. This book consists of selected papers presented at the Workshop. We would like to thank the Scientific Committee for the generous support of recommending invited lectures and selecting the papers for this volume, as well as the members of the Organizing Committee for their help. The Workshop was made possible by the financial support of several sponsors that are listed below. It is also a pleasure to thank our colleague Enrico Gregorio for his invaluable help of this volume.