The transformation of the mediaeval European image of the world in the period following the great discoveries of the 15th and 16th centuries is the subject of this work. The first studies deal specifically with the emergence of the concept of the terraqueous globe. In the following pieces Dr Randles looks at the advances in Portuguese navigation and cartography that helped sailors overcome the obstacles to the circumnavigation of Africa and the crossing of the Atlantic, and at the impact of the discoveries on European culture and science. Other articles are concerned with Portuguese naval artillery, and with attempts to classify the indigenous societies of the newly-discovered lands and to map the interior of Africa.