In succession to our former meetings on differential geometry a Colloquium took place in Debrecen from July 26 to July 30, 1994. The Colloquium was organized by the University of Debrecen, the Debrecen Branch of the Hungarian Academy of Sciences and supported by the Janos Bolyai Mathematical Society. The Colloquium and especially this proceedings volume received an important financial contribution form OMFB in the framework of the ACCORD Programme no. H9112-0855. The Organizing Committee was the following: S. Bacso, P.T. Nagy, L. Kozma (secretary), Gy. Soos, J. Szenthe (chairman) and L. Tamassy (chairman). It was pleasant to meet both the returning participants of our former colloquia and the numerous new guests. The Colloquium had 68 participants from 22 foreign countries and 18 from Hungary. At the opening we commemorated the 25th anniversary of the death of Otto Varga, the late Professor of the Debrecen University, one of the founders of Finsler geometry, the master of many differential of our country. The programme included 10 plenary lectures from: P.B. geometers Gilkey, R. Miron, I. Kolar, B. Wegner, D. Lehmann, o. Kowalski, T. Otsuki, K.B. Marathe, M. Crampin, W. Sarlet and 68 short lectures in 3 sections. The meeting created an inspiring atmosphere for fruitful discussions between the participants. The historical sites of the town Debrecen and its famous surroundings offered ideal to get to know Hungarian cultural traditions and for evening programmes.