We give a description of the book Небеска механика (Celestial Mechanics), written by Milutin Milanković, a renowned Serbian scientist . This book was the first university textbook of celestial mechanics at the Belgrade University. In it motion of celestial bodies was for the first time treated by applying vector analysis. A digitised copy of the book has become accessible through the Virtual Library of the Faculty of Mathematics at http://elib.matf.bg.ac.rs.