This paper discusses a range of questions concerning the application ofsolvable Lie algebras of vector fields to exact integration of systems of ordinarydifferential equations. The set of \(n\) independent vector fieldsgenerating a solvable Lie algebra in \(n\) -dimensional space is locallyreduced to some “canonical” form. This reduction is performed constructively (usingquadratures), which, in particular, allows a simultaneous integration of \(n\) systems ofdifferential equations that are generated by these fields.Generalized completely integrable systems are introduced and their properties are investigated.General ideas are applied to integration of the Hamiltonian systems of differential equations.
