**Thesis Type:** Postgraduate

**Institution Of The Thesis:** Bursa Uludağ University, Fen Bilimleri Enstitüsü, Fen Bilimleri Enstitüsü, Turkey

**Approval Date:** 2016

**Thesis Language:** Turkish

**Student:** Meryem Bekler

**Supervisor: **Osman Bizim

In this work which consists of six chapters, modular forms and their applications are considered. In the first chapter, the relation between modular forms and the other mathematical areas are examined. In the second, third and forth chapters, some preliminary notations, definitions and theorems which are to be a basis for the next chapters are given. The Riemann sphere C and its automorphisms are defined and some properties of the sphere are given. Elliptic functions are defined and some examples and properties are given. In addition, modular group and its subgroups are defined. The fifth chapter is the main part of the work. In this chapter, weak modular functions and modular forms are defined, some examples for them are given. In the last chapter, applications for the modular forms are discussed.