I wanna make a dropdown-menu like the one in the attached picture in android I searched a lot but I Couldn’t find anything?
Could you tell me how to start?

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Android does not generally use a “dropdown-menu” like the one you have in your screenshot. I encourage you to learn the Android UI framework and stick to it.
In Honeycomb (the tablet UI), there is the “nav mode” of the action bar that will look a bit similar, though it is not designed to be a menu.