In this chapter we define and give the simplest examples of Riemann surfaces. We derive some basic properties of Riemann surfaces and of holomorphic maps between compact surfaces. We assume the reader is familiar with the elementary concepts in algebraic-topology and differential-geometry needed for the study of Riemann surfaces. To establish notation, these concepts are reviewed. The necessary surface topology is discussed. In later chapters we will show how the complex structure can help obtain many of the needed results about surface topology. The chapter ends with a development of various integration formulae.
KeywordsNormal Form Riemann Surface Holomorphic Mapping Meromorphic Function Fundamental Group
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