Modern Algebraic Geometry: Motivation (1)

In this video we give a motivation for Modern Algebraic Geometry by Hilbert's Nullstellensatz and Functioriality of the Spec Functor.
Note: In the Nullstellensatz on the rhs there should be an inclusion not $\in$.
There are be two kind of Algebraic Geometry Videos on my channel: Some exercises (which suppose more knowledge about schemes and AG) and some more lecture like videos building upon another. This belongs to the second category.
00:00 Introduction and Examples
02:30 Nullstellensatz
05:30 Prime Ideals and Functoriality
10:20 Zariski Topology and vanishing of functions.