Sulphuric acid has a tendency to form hydrates, small clusters containing a few water molecules, in the gas phase. Hydrate formation has a stabilising effect on the vapour as the pressure of sulphuric acid drops (relative to unhydrated vapor), decreasing the nucleation rate. In classical nucleation theories the hydration energies and the hydrate distribution are predicted assuming that hydrates can be described as liquid droplets having thermodynamic properties of bulk liquid. To obtain a better understanding of the structures and formation energies of the smallest clusters, we have performed nb initio density functional calculations of the mono-, di-, and trihydrates. The hydrogen bonds between the molecules are found to be strong. The more water molecules the hydrate contains, the clearer ring-like structure is formed. Comparison to classical values for the hydration enthalpies confirms that the properties of bulk liquid do not describe the properties of the smallest clusters too well. The energy barrier for proton transfer reaction H2SO4 . H2O --> HSO4-. H3O+ for mono- and dihydrate is high, and protonisation is unlikely to occur, but in trihydrate the protonisation has almost occurred and the barrier is very low. We also studied the singly protonised monohydrate, and found that while sulphuric acid forms H bonds with the OH parts, the hydrogen sulphate ion tends to bind with the O (S=O) part, and the second proton stays tightly in the ion.