The story itself is no better than your usual Hollywood romantic comedy: a woman on a fictional Greek island reads in her mother's diary about three lovers she has had, any one of which could be her father, whom her mother has never revealed to her. She invites the three men to her wedding, they reminisce, and the young woman decides with her partner that they don't want to get married after all. That's it in a nutshell - but it shows how much one has to suffer to get from one ABBA hit to the other.
Another problem with the musical is that it appears Johnson has taken the songs for the show from ABBA's Best of album. A string of hits is not a musical. Still, Johnson finds ways, no matter how unrealistic, to fit the hits into the dialogue, which really only exists to fill the silence between the songs.