Enumeration Degrees - Local and Global Structure

The local structure of the e-degrees refers to the e-degrees below $0^{\prime }$. These correspond precisely to the degrees of the ${\mathrm{\Sigma }}_2$ sets. We shall talk about enumeration reducibility, its connection to Turing reducibility as well as contrast the local structure of the e-degrees with that of the Turing degrees. After a survey of known results we shall end with our new work and some open questions.