Advisor:

Bent functions have connections into various areas of mathematics and computer science which makes them an interesting object to study. This thesis is meant as a comprehensive study summarizing many of the results published in the last 40 years. In the first chapter we will motivate the definition of bent functions before we discuss some basic properties in chapter 2. This is done with a special emphasis on the investigation of restrictions of bent functions to hyperspaces. The obtained results will be used in chapter 3 to deduce connections of bent functions to various other mathematical structures. Though most results are well-known, we present some new, compressed proofs. Chapter 4 presents four different constructions of bent functions. Besides the two classical methods proposed by Maiorana/McFarland and Dillon we study two recent constructions by Seberry and Carlet, the latter of which leads to some useful general results