You can't really use Java without knowing these packages in the standard API:
java.lang
java.util
java.io
And, to a lesser degree:
java.text
java.math
java.net
java.lang.reflect
java.util.concurrent
They contain a lot of classes you'll need to use constantly for pretty much any application, and it's a good idea to look through them until you know which classes they contain and what those are good for, lest you end up reinventing wheels.