The word put is used in a large number of phrasal verbs.
Put across
To put something across is to make it understood.
He failed to put his message across. (= He failed to convey his idea.)
People working in sales and marketing should be able to put themselves across well.
Put aside
To put something aside is to set it aside.
He was feeling sleepy, so he put his books aside and went to bed.
Put away
a) To put something away is to keep them in their proper place.
You must put away those toys when you have finished playing with them.
b) To put something away is to save them for later use.
She makes it a point to put away a few dollars each week.
c. To put something away is to discard it.
It is high time you put away those false notions.
d. Put away can also mean eat or drink a large quantity of food or beverages.
If he is really hungry he needs just two minutes to put away a full meal.
e) To put somebody away is to send them to jail.
They put him away for killing his neighbor.
f) To put an animal away is to subject them to mercy killing.
The dog was so badly wounded that the doctor had to put him away.
Put down
a) To put something down is to write it down.
b) To put somebody down is to suppress them.
The government called the military to put down the rebellion.
c) To put something down to something else is to attribute the former to the latter.
He put the mistakes down to carelessness.
c) To put somebody down is to regard or categorize them as..
He was put down as a chronic nuisance.
d) To put somebody down is to belittle them.
I hate men who put their wives down in front of visitors.