Although written in 1998, and no mention of the Singularity per se, it does mention living machines and artificial intelligence. I was also thrilled to see a couple of mentions of the "Galactic Internet"!
Seth Shostak has a very entertaining writing style that has inspired me. The book makes you laugh out loud at the profound humour whilst compelling you to read the next section. I read the book in less than a day and a half.
Every aspect of Extra Terrestrials are covered, from how planet systems form (this was written before we had discovered such an abundance of ET planets), to how life begins, how intelligence forms, how aliens would evolve physically, and what motives they would have to communicate with us. It describes the SETI mission in comprehensive detail, recounts the history of UFO conspiracy, and discusses the implications of picking up a signal. No stone is left unturned, yet the book never feels like it's going into too much detail.
I thoroughly enjoyed it, and will be keeping it for future reference even though I'm currently travelling around the world and have serious weight limitation!