This report describes the development of a servo-controlled superconducting transition edge bolometer (STEB) intended for use as a sensitive broadband far infra-red (FIR), i. e. =1 mm to 100 μm wavelength, detector. A STEB uses a constant current biased superconducting film held on its superconducting transition, where it has a very high temperature coefficient of resistance, as a temperature sensing element for the absorbing substrate. Radiation absorbed by the substrate can be detected by measuring the change in voltage across the superconductor. The STEB's described in this thesis have in addition a resistive heater mounted on the substrate which is used as part of a servoregulating system maintaining the temperature of the bolometer at a fixed point on the superconducting transition. The potential advantages of this arrangement are higher frequency response, greater dynamic range, improved linearity and a STEB which can be more easily held on the superconducting transition. The STEB's described in this thesis used Sn films mounted on sapphire substrates as temperature sensors. Following a general introduction and review of previous work, the principles of operation of the servo system are described together with the theory of the system response, noise and the radiation performance of the detector. A detailed description is given of the construction of the bolometer, the bolometer optics, cryogenic apparatus and the servo circuitry. Optimisation of-the absorption of radiation by the bolometer substrate is studied using a transmission line analogue model. Experiments establishing the validity of the model are also included. The measured performance of the constructed STEB's is given and compared with theoretical predictions. The measured noise performance was found to be considerably better than predicted. Finally, suggestions are made for future improvements in detector-performance.