Large amounts of energy from heat sources such as waste-eat and geothermal energy are available worldwide but their potential for useful power-generation is largely untapped. This is because they are relatively low temperature difference (LTD) sources, in the range from 100 to 200 °C, and it is thermodynamically diffcult, for theoretical and practical reasons, to extract useful work at these temperatures. This work explores the suitability of a Stirling engine (SE) to exploit these heat sources. Elsewhere much work has been done to optimise Stirling engines for high temperature heat sources, but little is known about suitable engine layouts, and their optimal design and operational aspects at lower temperature differences. With the reduced temperature difference, changes from conventional engine designs become necessary and robust solutions for this novel application have to be identified. This has been achieved in four major steps: identification of a suitable engine type; thermodynamic optimisation of operating and engine parameters; optimisation of mechanical efficiency; and the development of conceptual designs for the engine and its components informed by the preceding analysis. For the optimisation of engine and operating parameters a model was set up in the commercial Stirling software package, Sage, which also has been validated in this thesis; suitable parameter combinations have been identified. This work makes key contributions in several areas. This first is the identification of methods for better simulating the thermodynamic behaviour of these engines. At low temperature differences the performance of Stirling engines is very sensitive to losses by fluid friction (and thus frequency), adiabatic temperature rise during compression, and the heat transfer from and to the surroundings. Consequently the usual isothermal analytical approaches produce results that can be misleading. It is necessary to use a non-isothermal approach, and the work shows how this may be achieved. A second contribution is the identification of the important design variables and their causal effects on system performance. The primary design variable is engine layout. For an engine having inherently low efficiency due to the low temperature difference it is important to choose the engine layout that provides the highest power density possible in order to minimise engine size and to save costs. From this analysis the double-acting alpha-type configuration has been identified as being the most suitable, as opposed to the beta or gamma configurations. An-other key design variable is working fluid, and the results identify helium and hydrogen as suitable, and air and nitrogen as unsuitable. Frequency and phase angle are other design variables, and the work identifies favourable values. A sensitivity analysis identifies the phase angle, regenerator porosity, and temperature levels as the most sensitive parameters for power and efficiency. It has also been shown that the compression work in low-temperature difference Stirling engines is of similar magnitude as the expansion work. By compounding suitable working spaces on one piston the net forces on the piston rod can be reduced significantly. In double-acting alpha-engines this can be achieved by choosing the Siemens as opposed to the Franchot arrangement. As a result friction and piston seal leakage which are two important loss mechanisms are reduced significantly and longevity and mechanical efficiency is enhanced. Design implications are identified for various components, including pistons, seals, heat exchangers, regenerator, power extraction, and crankcase. The peculiarities of the heat source are also taken into account in these design recommendations. A third key contribution is the extraction of novel insights from the modelling process. For the heat exchangers it has been shown that the hot and cold heat exchangers can be identical in their design without any negative impact on performance for the low-temperature difference situation. In comparison the high temperature applications invariably require different materials and designs for the two heat exchangers. Also, frequency and phase angle are found to be quite different (lower frequency and higher phase angle) from the optimum parameters found in high temperature engines. Contrary to common belief the role of dead volume has been found to play a crucial and not necessary detrimental role at low temperature differentials. Taken together, the work is positioned at the intersection of thermodynamic analysis and engineering design, for the challenging area of Stirling engines at low temperature differences. The work extracts thermodynamic insights and extends these into design implications. Together these help create a robust theoretical and design foundation for further research and development in the important area of energy recovery.