This book aims to present the newest research in the fields of mathematics and mechanics done by outstanding Georgian scientists. mathematics and mechanics are fundamental sciences. Theories of mathematics and mechanics are the basis of modern technological improvements and, therefore, interest towards them are increasingly important. This book presents the latest works of outstanding Georgian scientist and mathematician, academician Nikoloz Muskhelishvili. Together with the works of N Muskhelishvili, his book includes the recent works of a number of modern Georgian scientists who work in the fields of mathematics and mechanics.