Indefinite Article is Not Used Before Abstract Nouns

The indefinite article is not used before abstract nouns.

• beauty
• happiness
• fear
• hope 
• death

except when they are used in a particular sense.

• He was pale with fear.
• Some children suffer from a fear of the dark.

Materials are Considered Uncountable Nouns

Materials (glass, wood, iron, stone, paper, cloth, wine, coffee, tea &c.) are considered uncountable. But many of these nouns can also denote one particular thing, and then take an article:

Windows are made of glass but Have a glass of wine.
We write on paper but I've got a (news)paper.
Iron is a metal but I use an electric iron.

Some, any, a piece of, a lot of &c., are often used.

• Would you like some coffee?
• I want a piece of wood.

Indefinite Article is Not Used Before Uncountable Nouns

The indefinite article is not used before uncountable nouns.

The following nouns are singular and uncountable in English.

• advice
• information
• news
• baggage
• luggage
• furniture

They are often preceeded by: some, any, a little, a lot of, a piece of &c.

• I'll give you a piece of advice.
• You need some more furniture.
• There isn't any news.

Knowledge is also considered uncountable, but when used in a particular sense takes the article:

• A knowledge of languages is always useful.
• He has a good knowledge of mathematics.

Hair (all the hair on one's head) is considered uncountable, but if we consider each hair separateley, we say: a hair, two hairs &c:

• She has black hair
• The fisherman used a hair to tie the feather to the hook

Indefinite Article is Not Used Before Plural Nouns

The indefinite article is not used before plural nouns.

The indefinite article has no plural form. Therefore the plural of 'a dog' is 'dogs'.

Indefinite Article 'a' can be Placed before Mr/Mrs/Miss

The indefinite article, a, can be placed before Mr/Mrs/Miss + surname

For examples:

• a Mr Smith
• a Mrs Smith
• a Miss Rihana

'a Mr Smith' means 'a man called Smith' and implies that he is a stranger to the speaker.

'Mr Smith', without a, implies that the speaker knows Mr Smith or knows of his existence.

Indefinite Article is Used in Exclamations

The indefinite article, a or an, is used in exclamations before singular, countable nouns.

• What a hot day!
• What a pretty girl!
• Such a pity!

but

• What pretty girls!
• What big dogs!

(plural nouns, so no article)

Indefinite Article is Used with Few and Little

The indefinite article, a or an, is used with few and little.

a few means a small number, or what the speaker considers a small number
a little means a small amount, or what the speaker considers a small amount

So that ' a little time' can mean days or years, depending on the speaker; and 'a few friends' can mean two or three, or twenty or thirty.

only placed first: 'only a few/only a little' emphasizes that the number/ quantoty really is small -- in the speakers's opinion.

Few and Little can also be used without article but then have an almost negative meaning, and can usually be replaced by hardly any.

For examples:

• 'We had little time for amusement' implies that we were always busy.
• 'Few people know this' = It is almost unknown.

Indefinite Article is Used in Expression of Price, Speed, Ratio

The indefinite article, a or an, is used in expression of price, speed, ratio &c.

For examples:

• fivepence a kilo
• tenpence a dozen
• four times a day
• sixty kilometres an hour
• a pound

Indefinite Article is Used in Certain Numerical Expression

The indefinite article, a or an, is used in numerical expression.

For examples:

• a couple
• a dozen
• half a dozen
• a score 
• a gross
• a hundred
• a thousand 
• a million
• and a lot of
• a great many of 
• a great deal of

Indefinite Article is Used With Noun Complement

The indefinite article, a or an, is used with a noun complement. This includes names of professions:

For examples:

• He is a doctor
• She is a teacher
• She is a good girl
• He became a great man.

Indefinite Article is Used Before Singular Countable Noun

The indefinite article, a or an, is used before a singular countable noun which is used as an example of a class of things:

For examples:

• An elephant never forgets.
• A palm tree is usually very tall. 
• A cow has horns (i.e. All cows have horns).

Indefinite Article is Used Before Singular Noun

The indefinite article, a or an, is used before a singular noun which is countable (i.e. of which there is more than one) when it is mentioned for the first time and represents no particular person or thing.

For examples:

• A dog is an animal.
• A cat can catch a mouse.
• I see a man.
• A house has a roof.

The Indefinite Article

The indefinite article is a or an. The form a is used before a word beginning with a consonant, or a vowel sounded like a consonant.

For examples:

• a table
• a university
• a useful thing

The form an is used before words beginning with a vowel (a, e, u, i, o) or words beginning with a mute h:

For examples:

• an hour
• an egg
• an apple

It is the same for all genders:

• a man
• a woman
• an actor
• an actress