I would like to know the exceptions to the rule for the usage of the article "an."

Also please tell me why is it wrong to say "He is an European."

We've had this question a few times, here are the links: Articles?, "a" and "an", When to use 'the, an, a' Words that are articles

It's 'A European' because 'European' starts with a vowel.
For the usage of "a" or "an", what really matters is the first SOUND of the following noun.

We say: a car, a pen, a man. The sounds following "a" are consonant sounds.

So: an elephant, an animal, an umbrella. In this case, the initial sounds after "an" are vowel sounds. We say an umbrella, but a university (/j/ sound), a house, but an hourglass (/a/ sound). So we have to say "a European" because it is pronounced /juro'pian/).

Sorry if the phonetic symbols do not exactly match the sounds. I used approxinated ones with common letters.

Hope this helps! Emotion: smile
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He is European

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He is a European.

He is an Australian.