The Geodetic network of Lesotho as established by the Directorate of Overseas Surveys in the 1950's, has been known to have distortions of several meters in some areas. This network is still very much in use today. Several altcmpts were made to strengthen the DOS network. but these attempts were not used for a complete readjustment. The South African Control net, which completely surrounds Lesotho, has recently been readjusted so as to bring it into sympathy with the WGS reference system used by GPS. It has become urgent to similarly update the Lesotho control system, to enable economical use of GPS surveying methods. This thesis addresses the problems of updating the Lesotho control system and also of bringing existing data onto the updated systcm. This thesis first reviews the historical background of Lcsotho and that of its geodetic net work. Different sets of data were collected and common points in the compared sets selected for the analysis. The South African readjustment was chosen as the standard, because it is the most recent, derived with the support of the new zero-order South African control net. The data sets were fitted to the reference system using conformal transformations from first up to fourth order. These comparisons were used to detect outliers. They revealed systematic distortions in the older data. which could be largely eliminated in the fourth-order transformation. The opportunity to update control point co-ordinates also gave an opportunity to revisit the existing choice of using two map panels of the Gauss Conform projection. The distortions involved in using a single Gauss Conform panel and also the UTM projection were investigated. A companson or all the methods and the recommendations concludes the section. Software was developed for transforming existing survey data onto the recommended updated reference system. The height system used in Lesotho is also reviewed because it forms part of the control net. The focus is on heights in relation to gravity. because that bears on the relation of published orthometric heights. with GPS-derived ellipsoidal heights. This section is mostly a literature review, starting with the theory of heights and gravity, proceeding onto the applied corrections and then showing what relations have been found. / Thesis (M.Sc.Sur.)-University of Natal, Durban, 2001.