Abstract: In this talk we briefly give the definition of Riemann surfaces and related properties. There are three parts. The first part is to give the definition of a Riemann surface with some examples (torus, Riemann sphere). And then the second part is to introduce the (Weil) divisors and their (complete) linear systems on a Riemann surface. Here we also give some properties and examples. Finally, we shall define the meromorphic 1-form and the canonical divisor class and give some examples.