You know What is Activity,Activities life cycle,about Service to run application in background, Intents, Broadcast Receivers, Data storage using files, sharedPreferences, databases, Maps......
Life is easy because we write the source code.....
There are a number of books available like Pro Android 2 (Apress), Beginning Android 2 (Apress), Professional Android 2 Application Programming (Wrox). You can start with any of these books...
Well, if you want to run Eclipse plugins, then you'll obviously need Eclipse. But for Android development in general (which is what is discussed here), Eclipse is not needed.