Setting Up the Image Gallery With Albums

I get it how to make a page make a group of pictures in the form of gallery, so that when someone cicks on the picture Listbox pops up.
Of course it is possible to generate more than one such pages.

However, what I don’t get is how to combine all those pages into one page. One page has to be represented with a thumbnail picture and a title.
Then, when someone clicks on a thumbnail, a specific page has to open with a set of pictures that belong to that page.

TO sum up – I am trying to make the same functionality as with Facebook albums ie. you have one central page/repository and different albums (thumbnails) with title. When a user clicks on an album, the page with corresponding pictures opens, and a user can view the picture.

I recently started working with WordPress, so sorry if the following is not correct, but I can’t imagine that this functionality is not implemented in WordPress. It is in my opinion a functionality everyone would like to have and I see it as a an elementary for the tool that has so many users as WordPress. I tried to find a plugin that does exactly this, but couldn’t find anything.

Looking forward to constructive suggestions and answers.