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Where can I find a good construction (book, notes, videotapes on youtube ...) about $$H_{1}(R,\mathbb{Z}).$$ Where R is a Riemann surface closed.

In fact, I need a little more ... a reference on Rham cohomology would also be helpful! I need to learn Sheaf Cohomology.

Thank you.

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    What is $R$ here? What kind of cohomology are you thinking about? – 2017-01-15
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    @DanielRobert-Nicoud I edited to improve the question. thank you! – 2017-01-15
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    For coefficients in $\mathbb{Z}$, deRham cohomology is not what you are looking for. Singular cohomology is more suited. I am unsure about sheaf cohomology (I am ashamed to say that I have never really learned it) – 2017-01-15
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    Also, it is standard to write $H^1$ for cohomology, and $H_1$ for homology. – 2017-01-15
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    I know it's different things ... I've read a little about it in the past. But I wanted to read more closely at this time. – 2017-01-15
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    Well, singular and deRham cohomology are very closely linked: for smooth manifolds, deRham cohomology is canonically isomorphic to singular cohomology with coefficients in $\mathbb{R}$. – 2017-01-16
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    For sheaf cohomology you can take a look in the book of Forster, lectures on Riemann surfaces. – 2017-01-16

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