Can a user access to S3 be controled at Bucket and Object level?

Question

A AWS user can be given access to S3 by giving the appropriate permissions. Say the user is granted S3FullReadWrite permission through IAM.
But then, can the users be restricted to write to few buckets/objects only not all of them.

Other way put, can permissions be give/assigned to S3 Objects directly.

Edit: I think I found what I am looking for from the answer below. S3 ACL is what I have to look at.

Answer 1

There is a concept called Least Privilege which is very important, basically you give you users the rights they need and not more.

You have also the ability to add a Deny Action on certain resources, see the following diagram.