above and over

1) “higher than”: above or over
Above and over can both mean “higher than”. Above is more common with this meaning.
The water came up above/over our knees.
Can you see the helicopter above/over the palace?

2) “not directly over”: above
We use above when one thing is not directly over another.
We’ve got a little house above the lake. (Not over the lake).

3) “covering": over
We prefer over when one thing covers and/or touches another.
There is cloud over the South of England.
He put on a coat over his pyjamas.
We use over or across when one thing crosses another.
The plane was flying over/across Denmark.
Electricity cables stretch over/across the fields.

4) measurements: above
Above is used in measurements of temperature and height, and in other cases where we think of a vertical scale.
The temperature is three degrees above zero.
The summit of Everest is about 5000 metres above sea level.
She's well above average in intelligence.

5) ages, speeds, “more than”: over
We usually use over, not above, to talk about ages and speeds, and to mean "more than".
You have to be over 18 to see this film.
The police said she was driving at over 110 mph.
There were over 100,000 people at the festival.

6) books and papers
In a book or paper, above means “written before”.
The above rules and regulations apply to all students.
For prices and delivery charges, see above.
See over means “look on the next page”.
There are cheap flights at weekends: see over.

Michael Swan, Practical English Usage, Third Edition, Oxford University Press, 2006.