Monopoles on R^5

This thesis is motived by the wish to understand the structure of the moduli space of monopoles on R^5. Our approach to define monopoles is twistorial and we start by developing the twistor theory of R^5, which is an analogue of the twistor theory for R^3 developed by Hitchin. Using this, we describe a Hitchin-Ward transform for R^5, giving monopoles for the group SU(2). In order for us to construct monopoles we make use of spectral curves. Then, using those spectral curves we find a new system of equations, analogue to the Nahm's equations. Lastly, we prove that the geometry of the moduli space of solutions to this Nahm's equations carries a 2-symplectic structure.