Computer vision and robotics suffer from not having good tools for manipulating three-dimensional objects. Vectors, coordinate geometry, and trigonometry all have deficiencies. Quaternions can be used to solve many of these problems. Many properties of quaternions that are relevant to computer visions and robotics are developed. Examples are given showing how quaternions can be used to simplify derivations in computer vision and robotics. This research was sponsored by the Defense Advanced Research Projects Agency (DOD), ARPA Order No. 3597, monitored by the Air Force Avionics Laboratory under Contract F33615-78-C-1551. The views and conclusions contained in this document are those of the au- authors and should not be interpreted as representing the official policies, either expressed or implied, of the Defense Advanced Research Projects Agency or the US Government.