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I have done a classification using the semi-automatic classification plugin, and now, I would like to express each class in percentage of the study area (e.g. forest represent 20% of the study area and so one). Does anyone know how to get that ?

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Try the GRASS module r.stats. It allows to print out either area totals, or percents or area for each category. (Available in the Processing Toolbox)

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In raster structure you can count number of pixel which fall into a class, multiply for area of pixel then area_class_forest/area_of_raster. With vector structure you must have polygon then with a SQL query is possible obtain a table with class and percent area.

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