Methods for the calculation of the relative binding free energies of ligands to a protein are investigated and developed. The aim of these investigations was to improve the reliability and speed of free energy methods, such that they become practical tools for commercial rational drug design. To this end, the relative hydration free energy of water methane, and the relative binding free energies of halides to a calix[4]pyrrole derivative were investigated by three established free energy methods (Free Energy Perturbation (FEP). Finite Difference Thermodynamic Integration (FDTI) and Adaptive Umbrella WHAM (Ad-UmWHAM). The results of these applications showed that inconsistencies in sampling led to unreliable free energy predictions. To overcome these problems, a series of four new free energy methods were developed (Bivariate Multicanonical WHAM (BMW), Parallel Tempering Thermodynamic Integration (PTTI), Replica Exchange Free Energy Perturbation (REFEP) and Replica Exchange Thermodynamic Integration (RETI). These approaches all combined traditional free energy methods with generalised ensembles. Testing of these methods revealed that Replica Exchange Thermodynamic Integration was the superior of all seven methods. FDTI and RETI were then tested by calculating the relative binding free energies of a group of SB1-like ligands to p38 MAP kinase. The results of this test showed that RETI was still the superior method. This test also revealed that there were still sampling issues that needed to be resolved. A new Monte Carlo code was developed to run the tests on p38. The optimised data structure of the code led to a ten to twelve fold speed up compared to an established MC code. This, combined with the use of a large Linux Beowulf cluster, enabled each protein-ligand free energy calculation to be run within 1.5 days. We predict that, using the latest computers, these calculations could take less than 12 hours.