Java - Iterating over a Map which contains a List

First time here so I hope this makes sense!

I have a Map which contains a String as it's Key, and a List of Strings as it's Value. I need to iterate over all vlaues contained within each List within the Map.

So, first I want to get the Keys, which works:

Set<String> keys = theMap.keySet();

This returns me a Set containing all my Keys. Great :)

This is where I've got stuck - most of the info on the web seems to assume that the values I'd want returned from the Key would be a simple String or Integer, not another Set, or in this case a List. I tried theMap.values() but that didn't work, and I tried a forloop / for:eachloop, and neither of those did the trick.

Thanks y'all!