I propose a programme of precision tests of the Standard Model of particle physics to be carried out using the LHCb experiment at CERN. The proposal is focussed on studies of CP violation - differences between the behaviour of particles and antiparticles that are fundamental to understanding why the Universe we see today is made up of matter, not antimatter. The innovative feature of this research is the use of Dalitz plot analyses to improve the sensitivity to interesting CP violation effects. Recently I have developed a number of new methods to search for CP violation based on this technique. These methods can be used at LHCb and will extend the physics reach of the experiment beyond what was previously considered possible. I propose to create a small research team, based at the University of Warwick, to develop these methods and to make a number of precise measurements of CP violation parameters using the LHCb experiment. By comparing the results with the Standard Model predictions for these parameters, effects due to non-standard particles can be observed or highly constrained. The results of this work have the potential to redefine the direction of this research field. They will be essential to develop theories of particle physics that go beyond the Standard Model and attempt to address great unanswered questions, such as the origin of the matter--antimatter asymmetry of the Universe.