Aloupas is right about scheduling notifications. However, AlarmManager only works if the app has been run at least once to set the alarm and the phone hasn't been turned off. When the phone reboos/turns off, AlarmManager loses all of its pending stuff and they don't re-inflate when the system turns back on. I'd recommend the actual Android documents to check about Notifications in more broad sense, since there are a lot of types and a lot of solutions. Be warned, this stuff is dense, advanced, and finnicky as you move from API to API.
http://developer.android.com/guide/topics/ui/notifiers/notifications.html
There's also another thought: push notifications. If you want to manually alert your users about something (new levels added, double XP weekend, etc.), you'd want to register your app for push notifications. The easiest platform for managing this would be Parse. Parse is a flexible and easy to use HTTP library, and it includes DB support on Android, so it's a two-for-one. It also supports push notifications out of the box.
https://www.parse.com/
Cheers.