  These are expanded notes from lectures on the geometry of spherical varieties
given in Sanya. We review some aspects of the geometry of spherical varieties.
We first describe the structure of $B$-orbits. Using the local structure
theorems, we describe the Picard group and the group of Weyl divisors and give
some necessary conditions for smoothness. We later on consider $B$-stable
curves and describe in details the structure of the Chow group of curves as
well as the pairing between curves and divisors. Building on these results we
give an explicit $B$-stable canonical divisor on any spherical variety.

Algebraic Geometry