The book originally appeared as part of Springer’s excellent "Essential" series, and this new revised edition includes an extended chapter on Analytical Geometry and extra chapters on Barycentric Coordinates and Worked Examples. The chapter on Barycentric Coordinates forced me to return to one of my favourite books A vector Space Approach to Geometry by Melvin Hausner. This contains a wonderful explanation of balancing masses and how the results lead to barycentric coordinates. It also illustrates how area and volume are a natural feature of vectors. The chapter on Worked Examples draws upon some material from my recent book Geometry for Computer Graphics.