Adapter is an interface, you re trying to instantiate an interface(which is not possible in Java), you should create a class that implementes Adapter and write your code or use one of the already provided classes like SimpleArrayAdapter, CursorAdapter, etc. My recommendation would be, create a class that extends from BaseAdapter if you want a specific layout in your views and some unique functionality for it.
You can look at this question for a better understanding on how to implement your own adapter. How to customize listview using baseadapter
Hope it Helps!
Regards!