"Apocalypse" is Greek for "revelation," but has come to mean the end of the world thanks to the Apocalypse of St. John, better known as The Book of Revelations. "The Singularity" is the idea that our technology (specifically, our information/intelligence/computer technology) will soon improve at such a rate that it will be incomprehensible to us, and ultimately lead to an unpredictable event that will so alter us or the world that we will be unrecognizable. Popularized by Ray Kurzweil, its roots were laid out in a 1993 paper by Vernor Vinge, who noted that the key element of the Singularity would be "technological runaway." Anticipation of the Singularity has since become the central tenet of Trans-Humanism.
"What Is the Singularity?" Vernor Vinge
Planet of the Apes, film, Rod Serling (NB The film varies significantly from the original novel by Pierre Boullé)
“By the Waters of Babylon,” Stephen Vincent Benét
Marooned in Realtime, Vernor Vinge
Childhood’s End, Arthur C. Clarke
On the Beach, Nevil Shute
A Canticle for Leibowitz, Walter M. Miller, Jr.
The Stand, Stephen King
The Apocalypse of St. John (aka The Book of Revelations), traditional