Basic properties of Fano varieties

We discuss families of Fano varieties and prove their many basic properties
as in Chapter 2 of [6]. We also discuss some of the vanishing results proven by
Shepherd-Barron in his paper on Fano threefolds [7]. We introduce the three
basic invariants:  (Picard number), i (index) and d (degree). We prove their
basic properties.
Finally, we present some of Mori’s results on Fano varieties over fields of
characteristic zero; see Debarre’s book Chapter 4 (and especially 4.3) [3, Cor.
4.18]. For instance, we prove that Fano varieties over C are (topologically)
simply connected.