Hi and welcome to Android Forums.
There are a number of approaches here. My first thought was to present a Treeview - this is an expandable list which can accommodate an arbitrary level of list expansion
Code:
Root
|
----> Level 1
|
----> Level 2
|
.
|
----> Level N
But amazingly, and I'm astonished by this, there is no Treeview component provided in the Android UI library. The best you can do is to use ExpandableListView, which only accommodates two levels of list expansion.
But the Internet has yet again provided, and it seems like other people have implemented such a component. See here for a starting point -
https://stackoverflow.com/questions/3159758/suggestions-for-building-a-treeview-control-in-android
If you don't want to do it this way, then you could go for the classic file explorer type of approach - this is where you display icons representing the folders, and when tapped, they drill down into the folder contents, just like the Windows explorer application does. You will probably have to use something like a GridLayout for this, but it should be fairly straightforward.