1. In English, the two indefinite articles are a and an. Like other articles, indefinite articles are invariable. You use one or the other, depending on the first letter of the word following the article, for pronunciation reasons. Use a when the next word starts with a consonant, or before words starting in u and eu when they sound like you. Use an when the next word starts with a vowel (a,e,i,o,u) or with a mute h.
1.1. EXAMPLE
1.1.1. A boy
1.1.2. An apple
1.1.3. A helicopter
1.1.4. A university
2. The indefinite article is used to refer to something for the first time or to refer to a particular member of a group or class. Some use cases and examples are given below. Use a to refer to something for the first time.
2.1. EXAMPLE
2.1.1. Would you like a drink?
2.1.2. I've finally got a good job.
3. NAMING MEMBERS OF A GROUP
3.1. Use a with names of jobs.
3.1.1. EXAMPLE
3.1.1.1. John is a doctor.
3.1.1.2. He wants to be a dancer.
3.1.1.3. Mary is training to be an engineer.
3.2. Use a with nationalities and religions in the singular.
3.2.1. EXAMPLE
3.2.1.1. John is an Englishman.
3.2.1.2. Kate is a Catholic.
3.3. Use a with the names of days of the week when not referring to any particular day.
3.3.1. EXAMPLE
3.3.1.1. Could I come over on a Saturday sometime?
3.3.1.2. I was born on a Thursday.
4. Use a to refer to an example of something.
4.1. EXAMPLES
4.1.1. The elephant had a long trunk .
4.1.2. The mouse had a tiny nose .
4.1.3. It was a very strange car .
5. Use a with singular nouns after the words 'what' and 'such'.
5.1. EXAMPLES
5.1.1. What a lovely day !
5.1.2. She's such a beautiful girl .
6. Use a meaning 'one', referring to a single object or person, or a single unit of measure. In these sentences using "one" instead of the indefinite article is grammatically correct. It will add emphasis to the number, and contrast with other numbers.
6.1. EXAMPLE
6.1.1. I'd like an orange and two lemons please.
6.1.2. I'd like one orange and two lemons please.
6.1.3. I need a kilogram of sugar.
6.1.4. I need one kilogram of sugar.
6.1.5. You can't run a mile in 5 minutes!