A stroll in the mathematical world. This is neither an elementary introduction to the theory of singularities, nor a specialized treatise containing many new theorems. The purpose of this little book is to invite the reader on a mathematical promenade. We pay a visit to Hipparchus, Newton and Gauss, but also to many contemporary mathematicians. We play with a bit of algebra, topology, geometry, complex analysis, combinatorics, and computer science. Hopefully, motivated undergraduates and more advanced mathematicians will enjoy some of these panoramas.

#### English

This pdf book is available *free of charge* here (37 Mo), or on Arxiv, or on the website of ENS Éditions. Reviews by

Serge Tabachnikov, from the Math Intelligencer,

Damien Mégy, from the Gazette des mathématiciens,

Fernando Gouvea from the Mathematical Association of America,

Rafe Jones, from the Notices of the American Mathematical Society,

Alex Kontorovich, from the American Mathematical Monthly,

Frank Swetz, from the American Association of America,

Evelyn Lamb, from Mathematical Reviews,

Vicente Munoz, from the European Mathematical Society.

The LaTeX source files can be downloaded here (170 Mo).

A printed version is available for sale at ENS Éditions (27 €).

This book is published under a Creative Commons CC0 license.

#### Turkish

I am very proud that a Turkish translation is available. Warm thanks to Betül Tanbay, Ferit Öztürk, Ahmet Feyzioǧlu and Arkadaş Özakın and to the Turkish Mathematical Society.

#### Russian

A Russian translation is also available : Математическая прогулка с осмотром особенностей. Thanks to Evgeny Smirnov, for the translation, to Serge Lvovski for double checking this translation, to Vadim Radionov for the layout, and to Victor Klepsyn for suggesting all of this !

#### Portuguese

A Portuguese translation is also available.