When to use the indefinite article 'an'

The indefinite article is used:

1 to state the occupation of a person

e.g. He is an engineer.

2 in front of words with vowel sounds

e.g. An apple, an elephant, an iron, an owl, an urn, an unused pen, an hour, an honour, an heir, an honest boy

Although the following words begin with vowels, there are no vowels involved.

a university, a uniform, a one-arm bandit, a unicorn