- The purpose of this publication is to present some Notes from a Diary of a brilliant Romanian mathematician, Gheorghe Vranceanu, the discoverer of non-holonomic spaces. In the 60-70 ties, he was considered as the most important scientist in Geometry. Gheorghe Vranceanu published over 300 articles and many books in Differential Geometry, was a member of Romanian Academy, president of its Mathematics Section and Vice-president of the International Union of Mathematicians. Vranceanu was a student of Levi Civita, studied at Harvard and Princeton, worked with Elie Cartan, G.D.Birhoff, O.Veblen and received many honorary degrees from Universities in Romania, Italy, Belgium. The Notes cover a time interval of four years 1940-1944 and are written in the Romanian language.