Which sentence is correct?
I´m civil engineer or I´m civil engineering. I don't see any difference.

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Answer

Engineering is a subject matter. The people who work in that area are engineers. So a human can't BE civil engineering, but can be a civil engineer. You can say you WORK IN civil engineering however.

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The most native-sounding / natural-sounding options:
- I am a civil engineer (best)
- I work in civil engineering
- I work as a civil engineer

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I am a civil engineer, or I am in civil engineering.

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I am a civil engineer. 
I am studying engineering.
I am doing civil engineering.