In this mathematical autobiography, Chaitin presents a technical survey of his work and a non-technical discussion of its significance. The volume is a companion to the earlier collection of Chaitin's papers "Information, Randomness and Incompleteness" also published by World Scientific.

Examines the global qualitative behaviour of flows and diffeomorphisms. The book studies the fundamental theory and method of dynamical systems, emphasizes the global non-hyperbolicity and introduces some new results obtained by Chinese mathematicians which may not be widely known.