• indefinite: a, an
• definite: the
• zero

http://www.bbc.co.uk/learningenglish/english/course/lower-intermediate/unit-8/session-2/activity-3

We use the definite article with abstract uncountable nouns when the noun is used to refer to specific example of that noun.

http://www.bbc.co.uk/learningenglish/english/course/intermediate/unit-16/session-2/activity-3

The definite article is used when both the speaker and listener know what is being talked about or to identify a particular thing.

http://www.bbc.co.uk/learningenglish/english/course/upper-intermediate/unit-11/session-1

Indefinite articles, a and an, are not used with plural nouns or uncountable nouns. They are used

• when a singular countable noun is talked about for the first time,
• when classifying, describing and generalizing,
• in exclamations following words such as 'what' and 'such',
• in expressions like: 'a kind of', 'a sort of' and 'a type of'.

http://www.bbc.co.uk/learningenglish/english/course/upper-intermediate/unit-10/session-1

There are different types of nouns that don't require an article.

• plural and uncountable nouns for generalisations
• proper nouns
• when talking about the normal role of an instituion
• times of day, year and named holidays and special days/festivals

http://www.bbc.co.uk/learningenglish/english/course/upper-intermediate/unit-9/session-1