This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.

The editors are mathematicians whose work is well known (Dani in dynamics and ergodic theory, and Papadopoulos in geometry and topology of low dimensions). They are the authors of many research articles and monographs, and they edited several books. They have a broad view on the current research on geometry, on the history of the subject and on its impact in modern research. Dani is the editor-in-chief of Ganita Bharati (Bulletin of the Indian Society for History of Mathematics).