This thesis describes a detailed investigation into the process of laser-wakefield acceleration (LWFA) for the generation of high-energy electron beams using the hydrogen-filled capillary discharge waveguide. In only the second experiment to be performed using the newly commissioned Astra-Gemini laser at the Rutherford Appleton Laboratory, electron beams were accelerated to energies greater than 0.5 GeV by laser pulses of energy 2.5J and peak power of 30T\~T. The injec- tion and acceleration of electron beams was seen to depend on the state of the plasma channel for axial electron densities less than 2.5 x 1018 cm -3. With the aid of simulations performed using the code WAKE it was found that the plasma channel allows the laser pulse to maintain its self-focussed spot size along the length of the capillary even below the critical power for self-guiding. It was found that the threshold laser energy required for the production of elec- tron beams was reduced by the use of an aperture placed early in the laser system. This was attributed to the increased energy contained in the central part of the focal spot of the laser. A short paper on this work was published in Physical Review Special Topics - Accelerators and Beams and a longer paper was published in the New Journal of Physics. Transverse interferometry was used to measure the electron density of the plasma channel used in the Astra-Gemini experiments. An imaging system was devised which used cylindrical optics to increase the field of view of the capillary longitudinally, whilst maintaining the trans- verse resolution. The measured properties were consistent with previous measurements made by Gonsalves et al. [J]. The observed longitudinal variations in the plasma channel parameters were not found to be significant enough to affect the injection process.