This book contains the first complete English translation of Caspar Wessel's paper from 1797 "On the Analytical Representation of Direction". The paper has become famous because it gives the first geometric interpretation of the complex numbers. As the complete translation will show, it is also remarkable for the analytical representation of directions (vectors) in space and the elegant analytic solution of plane and spherical polygons. Wessel's essay is prefaced by two historical papers on the person Caspar Wessel and his work. They shed much new light on this first important Norwegian mathematician and sets his work on "directions" in its proper historical context. Among other things it is shown that the idea of using complex numbers to represent directions in a plane occurred to Wessel as early as 1787 in connection with his work as a surveyor. Moreover the papers address the question why Wessel's essay remained without influence.