From a historical point of view, the theory we submit to the present
study has its origins in the famous dissertation of P. Finsler from 1918
([Fi]). In a the classical notion also conventional classification,
Finsler geometry has besides a number of generalizations, which use the
same work technique and which can be considered self-geometries:
Lagrange and Hamilton spaces. Finsler geometry had a period of
incubation long enough, so that few math- ematicians (E. Cartan, L.
Berwald, S.S. Chem, H. Rund) had the patience to penetrate into a
universe of tensors, which made them compare it to a jungle. To aU of
us, who study nowadays Finsler geometry, it is obvious that the
qualitative leap was made in the 1970's by the crystallization of the
nonlinear connection notion (a notion which is almost as old as Finsler
space, [SZ4]) and by work-skills into its adapted frame fields. The
results obtained by M. Matsumoto (coUected later, in 1986, in a
monograph, [Ma3]) aroused interest not only in Japan, but also in
other countries such as Romania, Hungary, Canada and the USA, where
schools of Finsler geometry are founded and are presently widely
recognized.