**Thesis Type:** Postgraduate

**Institution Of The Thesis:** Uludağ Üniversitesi, Turkey

**Approval Date:** 2010

**Thesis Language:** Turkish

**Student:** HATİCE ÖZBAY

**Supervisor: **İSMAİL NACİ CANGÜL

In this thesis, several properties and usage areas of Euler numbers and polynomials are given. The thesis consists of three chapters. In the first chapter, the preliminary notions which are to be used in later chapters are given. In the second chapter Euler numbers and polynomials are defined and relations to calculate them are considered. Also some properties of Euler numbers and polynomials and the relations between these numbers and polynomials are given. Finally the zeta functions of these numbers are studied and the relation between Euler numbers and Bernoulli numbers is given. In the third chapter, some further properties of Euler numbers and polynomials are given and especially, their congruences in the moduli powers of two are studied.