Degree Theory

In this chapter, we outline the main degree theories which we encounter in applications. We start with the Brouwer degree and then we consider its infinite dimensional extension, which is the Leray-Schauder degree. In Sect. 1.3, we examine the degrees for certain maps of monotone type, which appear in many boundary value problems. Finally, in Sect. 1.4, we see how the previous degrees can be extended to deal with multifunctions.