This week's book giveaways are in the iOS and Features new in Java 8 forums. We're giving away four copies each of Barcodes with iOS: Bringing together the digital and physical worlds and Core Java for the Impatient and have the authors on-line! See this thread and this one for details.
Why not just take a look at the Collection and Map javadocs to find out for yourself?
As for the question of why Map is not a Collection, well, admittedly one can argue reasonably that a Map should indeed be considered some kind of Collection. But the designers of the Collections Framework ultimately decided that it's better to think of a Map not so much as a collection of objects, but rather as a relation between two collections. That's why the Map interface gives you accessors for the two underlying collections: keySet() and values(). You can then perform all your usual Collection operations on each of those two collections.
(However, Map also has an entrySet() method that muddles this view a little bit. You can read about that method in the javadoc, if you're not already familiar with it.)