We review the canonical theory for perfect fluids in Euler's and Lagrange's formulations. The theory is related to a description of extended structures in higher dimensions. Internal symmetry and supersymmetry degrees of freedom are incorporated. Additional miscellaneous subjects that are covered include physical topics concerning quantization as well as mathematical issues of volume preserving diffeomorphisms and representations of Chern–Simons terms (= vortex or magnetic helicity).
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