This book is about all kinds of numbers, from rationals to octonians, reals to infinitesimals. It is a story about a major thread of mathematics over thousands of years, and it answers everything from why Hamilton was obsessed with quaternions to what the prospect was for quaternionic analysis in the 19^th century. It glimpses the mystery surrounding imaginary numbers in the 17^th century and views some major developments of the 20^th century.