Well some of these that have been mentioned are damn fine classic albums and I love them too, but some could argue that not all of them are concept albums in the way that I think cosmic the OP had envisaged, but I am not speaking for him, he’s more than capable. I will add a huge endorsement for Jethro Tull’s 1972 Thick as a Brick. I owned the vinyl of its predecessor Aqualung 1971, and a friend had Thick as a Brick. Aqualung was supposedly described as a concept album, which (according to Wikipedia, the ultimate authority in the universe?
), absolutely infuriated Ian Anderson, the band’s frontman and songwriter. Anderson rejected the notion and felt Aqualung was merely a collection of songs. So he set out intentionally to create a parody of concept albums and poke fun at progressive rock. Out came Thick as a Brick, containing one continuous track split over the two sides of the vinyl LP. I think it is brilliant and is definitely a concept album. Also goes well with University Flake in a billiard.