This text will acquaint the reader with the most recent advances in Finslerian geometries, i.e. anisotropic geometries, and their applications by the Japanese, European and American schools. It contains three introductory articles, one from each of these schools, giving a broad overview of basic ideas. Further papers treat topics from pure mathematics such as complex differential geometry, equivalence methods, Finslerian deformations, constant sprays, homogeneous contact transformations, Douglas spaces, submanifold theory, inverse problems, area theory, and more. This book completes the Kluwer trilogy on Finslerian Geometry by P.L. Antonelli and his associates. Audience: This volume will be of interest to physicists and mathematicians whose work involves quantum field theory, combination theory and relativity, programming and optimization. Mathematical biologists working in ecology and evolution will also find it useful.

Generalizations of Finsler geometry / M. Anastasiei and D. Hrimiuc — Finsler geometry inspired / L. Kozma and L. Tamâassy — Finsler geometry / H. Shimada and V.S. Sabæau — Summary and overview / P.L. Antonelli — Some remarks on the conformal equivalence of complex Finsler structures / T. Aikou — Deformations of Finsler metrics / M. Anastasiei and H. Shimada — The constant sprays of classical ecology and noisy Finsler perturbations / P.L. Antonelli — On the geometry of a homogeneous contact transformation / P.L. Antonelli and D. Hrimiuc — On Finsler spaces of Douglas type III / S. Bâacsâo and M. Matsumoto — Equations of motion from Finsler geometric models / R.G. Beil — On the theory of Finsler submanifolds / A. Bejancu — Finslerian fields / H.E. Brandt — On the inverse problem of the calculus of variations for systems of second-order ordinary differential equations / M. Crampin — Complex Finsler geometry via the equivalence problem on the tangent bundle / J.J. Faran, V — Lâevy concentration of metric measure manifolds / W. Gu and Z. Shen — Hypersurfaces in generalised Lagrange spaces / M. Kitayama — The notion of higher order Finsler space : theory and applications / R. Miron — Generalized complex Lagrange spaces / G. Munteanu — Gravity in Finsler spaces / S.F. Rutz and F.M. Paiva — Higher order ecological metrics / V.S. Sabau — Area and metrical connections in Finsler space / L. Tamâassy — Problem / L. Tamâassy — Finslerian convexity and optimization / C. Udriðste — On projective transformations and conformal transformations of the tangent bundles of Riemannian manifolds / K. Yamauchi.