This book investigates the Poncelet porism and its interconnections with contemporary research areas. The author, Vladimir Dragović, presents a comprehensive overview of current research surrounding the Poncelet porism, integrating dynamics of integrable billiards, algebraic geometry of hyperelliptic Jacobians, and classical projective geometry of pencils of quadrics. It details key classical and modern results and ideas related to the Poncelet theorem, accompanied by a historical analysis of classical concepts and their generalizations. Significant focus is given to the Griffiths and Harris program concerning Poncelet-type problems and addition theorems, aiming to elucidate higher-dimensional analogues and the synthetic approach to higher genus addition theorems.

The book is presented as a comprehensive exploration of advanced mathematical topics, suggesting it is aimed at researchers and advanced students in mathematics and theoretical physics. Its detailed coverage of specific areas like integrable billiards and algebraic geometry indicates a specialized audience. The emphasis on historical context and generalization points to a text that bridges foundational concepts with cutting-edge research, likely appealing to those seeking a deep understanding of the Poncelet porism and its multifaceted applications.