How can I listen to a whole album on iTunes?
Assuming you are using a Mac with a newer system and the latest iTunes do the following:


Go to Album view


Now move the cursor to an album which will "enable" a play button in the lower right corner. Hit the play button to play all songs of this album:


If you click once more on the album you will see the content of the album:


To see the content of another album click on it - this won't interrupt the playback of the first album:


To play the second album either 


move the cursor over the second album and click on the then enabled play button 
move the cursor over the cover of the "expanded" album and click on the then visible bigger blue-on-white play button





move the cursor over one of the titles of the "expanded" album and click on the then visible small blue play button