The purpose of the book is a dual one: to detail the nature and results of Tunguska investigations in the former USSR and present-day CIS, and to destroy two long-standing myths still held in the West. The first concerns alleged "final solutions" that have ostensibly been found in Russia or elsewhere. The second concerns the mistaken belief that there has been little or no progress in understanding the nature of the Tunguska phenomenon. All this is treated by the author in a scholarly and responsible manner. Although the book does present certain unusual findings of Russian and Ukrainian scholars, it is important to stress that this is not a sensational book; it is, rather, a serious exposition of the results of rational investigations into a difficult scientific problem. We are demonstrating the true complexity of the problem that is now entering its second century of existence. Simple meteoritic models cannot explain all the characteristics of this complicated event, and therefore certain so-called "unconventional hypotheses" about the nature of the Tunguska explosion are to be considered as well.

Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibility of an advanced textbook with the completeness of an encyclopedia. The basic ideas that Lie and Cartan developed at the end of the nineteenth century to transform solving a differential equation into a problem in geometry or algebra are here reworked in a novel and modern way. Differential equations are considered as a part of contact and symplectic geometry, so that all the machinery of Hodge-deRham calculus can be applied. In this way a wide class of equations can be tackled, including quasi-linear equations and Monge-Ampere equations (which play an important role in modern theoretical physics and meteorology).