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Recent progress in the development of methods by which to decelerate and manipulate the translational motion of Rydberg atoms and molecules in the gas phase using static and time-varying inhomogeneous electric fields~[1] has led to the experimental realisation of Rydberg atom optics elements including a lens~[2], a mirror~[3] and a two-dimensional trap~[4]. These experiments exploit the very large electric dipole moments associated with Rydberg Stark states, and have demonstrated the possibility to stop a seeded, pulsed, supersonic beam of atomic hydrogen travelling with an initial velocity of 700~ms$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ within 2~mm~($\sim 5 \mu$s) using electric fields of only a few kVcm$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$.\ With the goal of achieving complete control of a cloud of Rydberg atoms or molecules in three-dimensions, we have recently designed and constructed a three-dimensional electrostatic trap for these particles~[5]. The design of this trap will be presented along with the results of a series of experiments in which we have used the trap to confine, in three dimensions, a cloud of atomic hydrogen Rydberg atoms in states of principal quantum number around $n=30$. The dynamics of the Rydberg atoms in the trap have been investigated by pulsed field ionisation and imaging techniques. Under favourable conditions, trapping times on the order of 150~$\mu$s have been observed. An important conclusion from this work is that as the trapping times closely match the fluorscence decay time to the $\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}S1/2$ ground state, cold stationary samples of ground state atoms can be produced following Rydberg Stark deceleration.\ \begin{tabular}{lp{11.1cm}} {[1]} & S. R. Procter et al., \emph{Chem. Phys. Lett.}, \textbf{374}, 667 (2003).\ {[2]} & E. Vliegen et al., \emph{Eur. Phys. J. D}, \textbf{40}, 73 (2006).\ {[3]} & E. Vliegen and F. Merkt, \emph{Phys. Rev. Lett.}, \textbf{97}, 033002 (2006).\ {[4]} & E. Vliegen et al., \emph{Phys. Rev. A}, \textbf{76}, 023405 (2007).\ {[5]} & S. D. Hogan and F. Merkt, \emph{Phys. Rev. Lett.}, \textbf{100}, 043001 (2008).\ \end{tabular}