This volume contains invited lectures and selected research papers in the fields of classical and modern differential geometry, global analysis, and geometric methods in physics, presented at the 10th International Conference on Differential Geometry and its Applications (DGA2007), held in Olomouc, Czech Republic. The book covers recent developments and the latest results in the following fields: Riemannian geometry, connections, parabolic geometries, jets, differential invariants, the calculus of variations on manifolds, differential equations, Finsler structures, and geometric methods in physics. It is also a celebration of the 300th anniversary of the birth of one of the greatest mathematicians, Leonhard Euler, and includes the Euler lecture "Leonhardt Euler - 300 years on". The notable contributors include: A Asada, Manuel de Leon, Jurgen Eichhorn, J-H Eschenburg, and Ivan Kolar.