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We have studied free higher spin gauge fields through an investigation oftheir Hamiltonian dynamics. Over a flat space-time, their Hamiltonianconstraints were identified and solved through the introduction ofprepotentials, enjoying both linearized generalized diffeomorphism andlinearized generalized Weyl rescaling gauge invariance, motivating our study ofconformal invariants for higher spins. We built these with the Cotton tensor,whose properties (tracelessness, symmetry, divergencelessness; completeness,invariance) we established. With these geometric tools, a first order actionwas written down in terms of the prepotentials. It is manifestly invariantunder electric-magnetic duality which, with the gauge freedom of theprepotentials, completely fixes the action. This action is associated totwisted self-duality conditions.  With an interest in supersymmetric extensions, we began to extend this studyto fermions, similarly analyzing the spin $5/2$ massless free field, whoseprepotential also enjoys conformal gauge invariance. The spin $2$-spin $5/2$supermultiplet was considered, and a rigid symmetry of its action (achirality-duality rotation) was built to commute with supersymmetry. We alsoinvestigated the properties of a mixed symmetry field on a flat six-dimensionalspace-time, the so-called chiral $(2,2)$-form: Hamiltonian analysis,prepotentials, and a first order action associated to self-duality conditions.  Finally, we studied both fermionic and bosonic higher spin surface chargesover a constantly curved background space-time. The Hamitonian constraints arethe generators of gauge transformations. Plugging into them appropriate valuesof the gauge parameters (imposing a physical variation of the fields), theirfinite and non-vanishing on-shell values were computed and recognized asconserved charges of the theory. Their algebra was checked to be abelian.

Aspects of higher spin Hamiltonian dynamics: Conformal geometry, duality and charges