These are old-fashioned Superman stories with a modern spin. In the opening story Supes rescues some genetically modified scientists from falling into the sun. In doing so he absorbs far more solar radiation than his body can handle. The result is that it's going to kill him. This was all planned by arch nemesis Lex Luthor, who realized that while he's getting older Superman is not. And that there's no beating around the bush anymore. He wants Superman dead, even though he himself is in prison, on death's row.
Superman also reveals to Lois Lane that his secret identity is Clark Kent and even though he shows her the proof she still doesn't believe him. As a birthday present he gives her comparable super powers for a day so she knows what it's like to be him. During this time they are visited by time travelers from the future. They show a headline that says "Superman is Dead". There are also visits from "Supermen" of the future.
Volume 2 continues the story arc, with Superman preparing for his imminent death and even writing a Last Will. He also must provide for the zoo of creatures in his Fortress as well as help the bottle city of Kandor. The Earth is invaded by the square Bizarro world and we're reintroduced to that weirdness. While he's stuck there two survivors from Krypton have found their way to our world and bill themselves as Superman's replacements. But they want to transform Earth into a new Krypton and have a low opinion of mankind.
This is a great collection of stories, set outside the regular DC comics continuity. Highly recommended.