Which Currency can I use in Georgia?

According to Lonely Planet:

• Georgia’s currency is the lari (GEL). It has been fairly stable since it was introduced in 1995. One lari is divided into 100 tetri.
• Banknotes come in denominations of one, two, five, 10, 20, 50, 100 and 200 lari; coins run from one tetri to two lari.
• ATMs, generally accepting MasterCard, Visa, Cirrus and Maestro cards, are plentiful in cities and towns.
• There are also plenty of banks and small money-exchange offices in most towns and cities, where you can exchange US dollars, euros and
  sometimes sterling and the currencies of Georgia's neighbouring
  countries.
• You can make purchases with credit cards at some hotels, restaurants and shops, though less frequently outside Tbilisi.
• Common tipping practice in restaurants is just to round up the bill to the next round number.

As for exchanging money at the airport, there are 5 different banks and 6 ATMs that you could exchange money or withdraw money from. Each bank has it's own policy on the maximum amount of currency to exchange.

I was in Georgia a month ago and I have never seen any price in a currency different than Lari or a announcement that any other currency is accepted.

There are many exchange offices in Tbilisi and a couple in the airport. Exchange rate in the airport is not worse than in the city in general (and even better than in some places).

It seems that there is no maximum amount that you can exchange (I have exchanged up to 300€ without any problem). Be prepared to present your pass or other ID.