I read the Iliad for the first time maybe four months ago and I was shocked--like, seriously, kind of floored--at how badass it was. It's fast-paced, gripping, and--especially starting around Book III--fantastically violent and action-packed. There were also brief, lyrical domestic scenes which had a profound effect on me. Here you are, reading this bloody epic of war, destruction, revenge, and the gods, and then there's this tender scene between father, mother, and son, and you realize that even though this is a fictional work, it's fundamentally rooted in humans doing deeply recognizable and identifiable human things two and a half millennia ago.
I read the Fitzgerald translation and found it very worthwhile. The supplementary material provided much-needed cultural and stylistic context that enriched the experience considerably.
Edit: Realized I kind of replied to the wrong comment, and I think someone else answered your question--yes, these works are definitely mythological in nature. The battle of Troy itself was considered to be mythological until sometime after the 17th century (not an expert at all, so not even going to attempt to date this any better than that).
>Believe me, I've tried...
http://www.amazon.com/Iliad-Homer/dp/0374529051
http://www.amazon.com/Odyssey-Homer/dp/0374525749/
http://www.amazon.com/Aeneid-Everymans-Library-Virgil/dp/0679413359/
http://www.amazon.com/Tale-Genji-Penguin-Classics-Deluxe/dp/014243714X/
http://www.amazon.com/Three-Kingdoms-Chinese-Translation-Footnotes/dp/0804843937/
http://www.amazon.com/Republic-Plato/dp/0141442433/
http://www.amazon.com/Nicomachean-Ethics-Penguin-Classics/dp/0140449493
http://www.amazon.com/Lord-Rings-50th-Anniversary-Vol/dp/0618640150/
http://www.amazon.com/Dune-Frank-Herbert/dp/0441172717/
/r/chess
/r/hiking
/r/cookingforbeginners/
/r/writing
/r/photography
/r/learnprogramming
This is just stuff I came up with off the top of my head. The books alone will keep you busy for at least a couple months if you're a prodigious reader. There's pretty much no way you could possibly finish this entire list before September.