Nambu’s proposal suggests the generalization of the standard canonical formalism such that the phase space is extended to arbitrary dimensions including odd dimensions with an extended canonical structure typically represented by Nambu bracket as an extended form of Poisson bracket. In this chapter, a systematic approach to such a generalized canonical formalism is presented using mainly the language of differential forms from a geometrical viewpoint. Special emphasis is put to aspects of symmetries which characterize such an extended canonical formalism.