One of the most important areas of study in mathematics, physics and engineering involves scattering and the propagation of scalar and vector waves. This topic is very mathematical, which often obscures the physics and engineering of scattering and propagation. It is the goal of this author to introduce this topic in a manner where the emphasis is placed on the physical interpretations of the mathematics involved without losing the mathematical rigor. Lastly, a number of important developments in this field are discussed that have never been mentioned in books before as they are hidden...