Organizing photos on my phone

Add pictures to an album like this:

Create a new album

1. Open Photos.
2. Go to Albums and tap the Add button .
3. Tap New Album. Type an album name, tap Save, then choose the photos and videos that you want to add.
4. Tap Done.

Add to an existing album

1. Open Photos.
2. Tap Select, then tap the photos and videos that you want to add.
3. Tap the Share button , then tap Add to Album and choose an album.

I was about to write down steps, but I found the above list at this site:

Organize and find your photos on your iPhone, iPad, or iPod touch - Apple Support

I am not sure what you mean by "files within an album"? Ar you asking how to group related albums together by creating folders with subfolders?

Photos can only be added to albums - as described by Richard.

To organize the albums and to group related albums together, you can use folders - so you could have an folder "Pets", and inside albums "Dogs" and "Cats" and "Caray Birds". There is a hitch, however. On the iPhone or iPad we have to create the albums directly inside the folder where we want them to be. We cannot move the albums freely between the folders. But using the folders will shorten the list of albums and make much easier to find an album quickly.