Reddit reviews The Greek Myths: The Complete And Definitive Edition

You could try Robert Graves' accounts:
http://www.amazon.co.uk/The-Greek-Myths-Complete-Definitive/dp/0241952743/ref=sr_1_1?ie=UTF8&qid=1369646616&sr=8-1&keywords=greek+myths

Or more contemporary: Apollodorus, a Hellenistic scholar who tried to collate the myths in one volume:
http://www.amazon.co.uk/Library-Mythology-Oxford-Worlds-Classics/dp/0199536325/ref=sr_1_1?s=books&ie=UTF8&qid=1369646747&sr=1-1&keywords=apollodorus

Bear in mind though that many of the myths were continually changed, evolving and being re-written. There are no definitive versions.
You should probably also steer clear of calling them parables, as the word doesn't really apply.

I would point to Robert Graves' "The Greek Myths" it has extensive annotations which help greatly in understanding what's going on. I see from an Amazon search that Penguin seem to have combined several volumes into one book. It's a long read akin to a Labour of Heracles (one of the 10 - or was that 12? ;) ) but very worthwhile indeed, in my opinion.

http://www.amazon.co.uk/The-Greek-Myths-Complete-Definitive/dp/0241952743/277-3880124-2288040?ie=UTF8&*Version*=1&*entries*=0

https://www.amazon.com/Greek-Myths-Complete-Definitive/dp/0241952743

Robert Graves "The Greek Myths"