  The book can be divided in three parts: the Lagrange geometry of order $k$,
presented in the first three chapters, the geometrical theory of the dual
manifolds $T^{*k}M$ - chapters 4-7 and the geometry of Hamilton spaces of order
$k$ and their subspaces, contained in the last four chapters. They are studied
directly and as 'dual' geometry, via Legendre transformation.
