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This text gives the most recent results in Finsler and related geometries from the Miron school. Both pure and applied topics are covered. For example Higher-Order geometry, Hamilton and Cartan spaces, Legendre transformations, self-duality in Gauge fields, constant curvature spaces, Electromagnetics, Gravity theory, Black Holes, complex Finsler geometry and Finsler-Lagrange-Hamilton structures in control and optimization. There is also an article on Finsler Seismic ray theory which uses the software FINSLER based on MAPLE.