Sheaves ([H] Ch II.1), with a few ideas from [V] Ch 1.3 (universal properties), and [V] 1.4 (colimits) incorporated). Parts of Aug 24 and Aug 26 lectures.
Category Theory ([V] Ch 1.1-1.6 middle of P48). Parts of Aug 26 and Aug 31 lectures.
Schemes ([H] Ch. II.2). Parts of Aug 31 and Sep 2 lectures.