I know how to make the gradient and the logo. But I don`t know how to add all that different borders and how to add the refresh icon (that also has some custom border around it).
Instagram Action Bar:

How is that possible?
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You can do it by using a horizontal LinearLayout with 2 children, the left hand column with the logo and the right hand column with the refresh button. You can create a background drawable using the Shape XML:
http://developer.android.com/guide/topics/resources/drawable-resource.html#Shape