  Canonical quantization has taught us great things. A common example is that
of the harmonic oscillator, which is like swinging a ball on a string back and
forth. However, the half-harmonic oscillator blocks the ball at the bottom and
then it quickly bounces backwards. This second model cannot be correctly solved
using canonical quantization. Now, there is an expansion of quantization,
called affine quantization, that can correctly solve the half-harmonic
oscillator, and offers correct solutions to a grand collection of other
problems, which even reaches to field theory and gravity.
  This paper has been designed to introduce affine quantization; what it is,
and what it can do.
