I want my app to run things in the background, even when the user is donig other things on his Android

What should I look at to get started?

Is it Timer? http://developer.and开发者_开发技巧roid.com/reference/java/util/Timer.html

Or am I missing something else?

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You should use a Service:

http://developer.android.com/reference/android/app/Service.html