Can we create media folders and put them on a WordPress page?

We want to put a folder on a page containing media items (pictures, .pdf files, Word files, etc.) grouped together for user selection and download. For example, the user goes to the page and there is a picture of a folder on the page titled “Spring 2015.” They click on the folder and see the media items I have put in there relating to Spring 2015. Can I do this in WordPress? Maybe there is a way to do this in a plugin and put the folder on the page with short code?

Thank you very much for your help!