Abstract: Kasparov's KK-theory is a very interesting theory with various applications, such as extensions of $C^*$-algebras and the Novikov conjecture. We will discuss the basic definitions of KK-theory and see how it allows us to recover various properties of K-theory and K-homology such as Bott periodicity, as well as a nice formulation of the Atiyah-Singer index theorem. If time permits, I will also briefly discuss my own interest in KK-theory via the unbounded picture.