In 1925, R. Nevanlinna[1] established two fundamental theorems; in one stroke he initiated the modern research on the theory of value distribution, and laid down the foundation for its development ever since. Therefore, the first chapter will be devoted to a brief introduction to Nevanlinna theory1), and the last section of the chapter, as an illustration of the development, will discuss an important theorem by Osgood[1] and Steinmetz[1].