In 1872 Klein delared the Erlangen programme to understand various geometries in a unified manner as homogeous spaces of groups, then in 1920's Cartan invented the notion of espace généralisé (principal bundle with Cartan connection in modern terminology) to treat still group theoretically not only the homogeous spaces but also inhomogeous spaces such as Riemannian geometries, conformal or projective differential geometries.

We propose a Klein Cartan programme for differential equations in the framework of nilpotent geometry and analysis, which gives rise to a variety of interesting problems between the geometries and the differential equations.

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