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This MSc report discusses the attributes of W Ursae Majoris (W UMa) stars and an investigation into the Minimum Entropy (ME) method, a digital technique applied to the determination of their periods of variability. A Python code programme was written to apply the ME method to photometric data collected on W UMa stars by the All Sky Automated Survey (ASAS). Starting with the orbital period of the binaries estimated by ASAS, this programme systematically searches around this period for the period which corresponds to the lowest value of entropy. Low entropy here means low scatter (or spread) of data across the phase-magnitude plane. The ME method divides the light curve plot area into a number of elements of the investigators choosing. When a particular orbital period is applied to this photometric data, the resulting distribution of this data in the light curve plane corresponds to a speci c number of data points in each element into which this plane has been divided. This data spread is measured and calculated in terms of entropy and the lowest value of entropy corresponds to the lowest spread of data across the light curve plane. This should correspond to the best light curve shape available from the data and therefore the most accurate orbital period available. Subsequent to the testing of this Python code on perfect sine waves, it was applied, and its results compared, to the 62 ASAS eclipsing binary stars which were investigated by Deb and Singh (2011). The method was then applied to selected stars from the ASAS data base. / School of Environmental Sciences / M. Sc. (Astronomy)