Watch this series, you will understand the first lecture totally. Simon’s general terminology can be hard to understand. For example, he uses F as a field. But in the beginning, if you simply understand it as a real number (scalar), the rest is easy to catch. The whole idea is to expand your numbers into a space (from one dimension to n dimension.)

The axioms are starting point to define this space system. Therefore, watch Chapter 1 first, then go to the next video, see what cannot define a vector space. Then come back to this Essence of Linear Algebra and finish all the 15 videos.