Long-Term Timing of Millisecond Pulsars and Gravitational Wave Detection

(Abridged) This thesis presents long-term timing results on 20 millisecond pulsars (MSPs). It has been predicted that such timing may detect gravitational waves (GWs) - a major (but untested) prediction of general relativity. Our results demonstrate that most of the investigated MSPs have sufficient stability to enable such detection experiments. Furthermore, the timing data of the brightest few sources shows that timing at sub-100 ns precision may be achievable and that, therefore, GW detection within the next decade is likely. Finally, we use our data to place a strong limit on the strength of a predicted background of GWs.