I am able to delete Photos from the library but not from the albums

I'm not sure what you mean. Is it that you want to delete pictures from Library but leave them in albums? It that's it, then Russ New Boy is right.

Pictures aren't exactly "in" an album. When you "put a picture into an album," its name is added to a list of pictures to display together when the album is clicked, kind of like a music playlist, but for pictures. So two albums can both have the same picture name in their lists (like two playlists with the same song, and that picture will show up when you click either album, but there's only one picture file-- it's just on multiple lists. And when you remove a picture from an album, its name remains in the lists of other albums, and the file still remains in your Library. 

So albums give a specific view of your pictures. The picture of "Aunt Ethel at the Grand Canyon" can be in the "Aunt Ethel" album with other pictures of Aunt Ethel, and it can also be in the "Grand Canyon"  album with pictures of other people at the Grand Canyon. And it can be in a the "September 2015" album. Each album is pointing to a single file stored in the Photos Library, so having pictures in multiple albums takes up no more storage space. As you can imagine, this is very powerful in organizing pictures.

Those places called Library and Recents, etc, are not real albums--not like the ones you make yourself. These are special pre-set ways to view your pictures. The "LIbrary" view shows all the pictures in your Library in the order your pictures were taken. The "Recents" view shows all the pictures in your Library in the order they were added to the Library-- not necessarily in the order they were taken. This can't be changed. These albums always provide the same view so that, when something goes wrong or seems off, you (and we) can depend on them always showing the same thing, and there's no chance that someone snuck in and changed the order or removed pictures. 

So if you delete a picture from the Library or from Recents, it must be deleted from the phone. (Of course, it really goes into the Recently Deleted view, and you have 30 days to change our mind.) 

This is not possible. All photos in an album need to be in/ are selected from the library. If you delete a photo from the library it will delete the photo from every album that it is included in. It's just the way Photos is set up.