Q:

Difference between 上げる and 与える

I have some notes from many years back when I began to do Japanese. As you might expect, I am suspicious of my understanding at the time and of what I've written.
I have two verbs for "to give" and would like to check what the differences are.
上げる    give
与える    give

I also have
あげる    do a favour (not 'I' but 'they')

but I don't know what I meant by my english explanation. Does anybody recognise あげる as "doing a favour"?

A:

上げる is used generally and it is also polite.
If you want to say the same meaning in not polite way, you say やる（遣る）.
与える is used only when the upper rank person gives something to the lower one/ones. For example, a king gives something to the vassal/retainer.
あげる used in （し）て＋あげる is used in doing somebody a favor in doing something.
I'll show you some examples;
ごみを出すのを手伝ってあげる。I would help you take out the garbage. 
苦労話を聞いてあげる。I would hear your hard-luck stories.

