\input zb-basic \input zb-matheduc \iteman{ZMATH 2016c.00692} \itemau{Leng, Gangsong} \itemti{Geometric inequalities. Translated by Yongming Liu.} \itemso{Mathematical Olympiad Series 12. Hackensack, NJ: World Scientific (ISBN 978-981-4704-13-7/hbk; 978-981-4696-48-7/pbk). viii, 136~p. (2016).} \itemab The book addresses students who want to practice for a math Olympiad. The author presents geometric inequalities which take place in different polygons, circles or tetrahedron. The paper is structured into 11 chapters. Most of the chapters start with a 5 to 6 example set in which different methods of proving geometric inequalities, like Ptolemy's inequality, the area inequality, linear geometric inequalities, algebraic methods, inequalities for tetrahedron are explained. The examples are carefully picked and are useful for the method the author chose to highlight. At the end of each chapter, 5 exercises are to be solved. At the end of the book, the reader can find the solutions to the exercises. \itemrv{C\u{a}t\u{a}lin Barbu (Bacau)} \itemcc{G10} \itemut{geometric inequalities; olympiad; Ptolemy's inequality; area inequality; isoperimetric; tetrahedron} \itemli{doi:10.1142/9661} \end