Well, usually when one plays a very early g3, they also fianchetto that bishop, (otherwise what's the point?) and often play the king's knight to f3, and castle. When they do all of this it usually amounts to a King's Indian Attack type of setup, and there are books on that opening.
1.g3 book?????

What system do you want to play? Alekhine Reversed (1. g3 e5 2. Nf3), Reti (kingside fianchetto, Nf3 and c4), KIA, fianchetto d4-c4 openings, fianchetto d4 opening or what?
ChessBase can be used for making your own repertoire, and/or finding a player who plays the same as you want to play.
A BOOK ON 1G3 IS : "THE WHITE SNIPER MANUAL" BY CHARLIE STOREY 2012... PRICE $ 50.00 US DOLLAR...REAL EXPENSIVE COMPARED WITH OTHER TITLES...DON'T KNOW IF THE BOOKK IS THAT GOOD....

Can also transpose into a Catalan
This is your contribution after more than 11 years?

Got bamboozled by a 1 g3 player, googled to look for some theory to avoid this scenario from happening again in the future and ended up here without looking at the date/time of earlier posts. Looking at it, I think most of the theory on 1 g3 is found (transpositionally) in the lines mentioned in earlier posts such as the Reti, KIA, Barcza system, Hippo, English, Catalan, Double Fianchetto. To add something new to this is not easy: books on Flank openings may also help out : the books of Keene or Kotronias, or Euwe's series in earlier times. Books on unusual or off-beat openings may contain small chapters on 1 g3. ECO A has only one small subchapter dedicated to the immediate 1 g3 in A00. I found the dvd: Foxy opening Unusual openings - A repertoire for black against , b4, a3, f4, g3, g4 and Nc3 - dvd by Andrew Martin. So far, I haven't be able to find an extensive repertoire book for White on 1 g3. I'll need more time to do research on this.

Who's Andrew Martin?
ROFLMAO!
He's churned out not only a ton of videos already mentioned (Foxy, Chessbase, etc), but also a couple dozen books, mostly offbeat stuff like the Scandi, Budapest, etc, though he has a few main stream openings. The only real lemon of his is Kings Indian Battle Plans. Poorly organized!
A chess player not knowing Andrew Martin is like a baseball player not knowing who Babe Ruth is. Not by any stretch the best player in history, not even during his era, but such a well known old relic that all chess players know who he is/was.
It's like Anna Kournikova in tennis or Bon Jovi in music or Julia Childs in cooking.

I was wondering whether there was any book written on as I couldn't find any on the internet
Google Bobby Fischer and The Kings Indian Attack.
write notes, you will have your own book.
I don’t think of 1. g3 as a distinct opening. I used to play it back in the early 1980s. I would wait for Black to commit to some central pawn structure and then transpose into any of a dozen or so different options—often a Black opening with colors reversed.
Because of there being so many transpositional possibilities, I don’t recommend this to lower-rated players.
I was wondering whether there was any book written on 1.g3 as I couldn't find any on the internet