Thesis (MTech (Electrical Engineering))--Cape Peninsula University of Technology, 2018. / This research investigates the absorption spectra of rubidium and the feedback control of an external cavity diode laser. This research is a necessary prerequisite for laser (Doppler) cooling and trapping of rubidium atoms. Cooling rubidium atoms down to such low temperatures can be achieved using the Doppler cooling technique. Here a laser is tuned to remain resonant with a speci c atomic transition. To do this, the absorption spectra of rubidium must therefore be observed. All of the above require a reasonable knowledge about topics such as atomic physics, laser cooling and trapping, feedback control systems, and absorption spectroscopy. A discussion of these topics is provided. We have utilised an experimental setup which allowed for measurements of the Doppler broadened and Doppler free absorption spectra of rubidium, as well the analysis of the Zeeman e ect on the Doppler free spectra. The setup consisted of a saturated absorption spectrometer for high resolution spectroscopy and a Michelson interferometer for calibrating our measurements. In analysing the Zeeman e ect we added a set of Helmholtz coils to the saturated absorption spectroscopy arrangement to measure the splitting of the hyper ne energy levels. / French South African Institute of Technology (F'SATI) National Research Foundation