On the half-integral weight modular forms

Modular forms are have attention and popularity for many years. They have applications in many areas of mathematics and physics. In this study which consists of four chapters, modular forms of weight half-integral is introduced. In the first part, general and special linear groups have been introduced, some properties are discussed. In the second part, the modular group that has an important place in the definition of modular forms is given. In the third chapter, modular forms areinvestigated and some examples of modular forms are given. In the fourth and final chapter, half–integral weight modular forms are defined, some features are examined and examples are given. This study is a compilation.