Elementary Category Theory

I've been asked for an introduction to category theory, especially for people who are not advanced mathematicians. I've found a number of videos and other documents.

Two quick introductions -- what category theory is about and why it's useful.

Funny, but possibley unhelpful to the beginner:

A discussion on Quora:

A serious beginner's book on category theory:

And about the relationshipe between category theory, type theory, and set theory. Each of these has been touted as a possible foundation for mathematics. Set theory is the oldest, and best-known of these. Category theory are is starting to see serious use in the theory of programming languages. And type theory is one of the tools often used nowadays in formal verification of proofs.