Newton’s Universe used a simple number system we all know, the real numbers. The real numbers are not enough to understand the Space-time Universe. Einstein and Minkowski, imagined the Universe as a 4 Dimensional (4D) Space-time. In 1843 William Rowan Hamilton, had imagined a 4D Space he called Quaternions. This space was unique but not popular and was unfortunately forgotten. Quaternions, though forgotten, are the Space of our Universe. This book is On Quaternions. It will introduce you to Quaternion Numbers, and Arithmetic and Calculus. Then it will apply Quaternions to Newton’s Laws of Universal Gravity and the electron in the Atom.Quaternions bring Truth and Beauty to Physics. ...