The purpose of this book is at once modest and ambitious, namely, to provide a short introduction to algebraic geometry in space of three dimensions, to make clear its spirit, and to prepare the way for deeper study. This book will appeal to a reader who has read Maxwell's book on homogenous coordinates in a plane (to which this stands as a second volume) and is in the early stages of second year work at University, It will also be suitable for a class reader who has read further in mathematics generally, but has found the existing detailed accounts of this work too full or too specialised for their own needs, and is in need of an accessible introduction.