Integrating on a Riemann surface

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I would like to understand how one integrates on a simple example of a Riemann surface: $\mathbb{C}/\Lambda$ where $\Lambda$ is a lattice. As an example, how does one calculate $$ \int_{\mathbb{C}/\Lambda} f(z) dz $$ for some meromorphic function $f$ ? How does one identify it with some double integral on $\mathbb{R}$ or so ? If anyone has some illustrative example that would be very nice.