It is interesting that the Tbilisi Transport Company and the Toronto Transit Commission share the same abbreviation, i.e. the TTC.
Right off the top, the airport (TBS) is not connected to the airport via the Metro. The closest Metro stop to the Airport is Varketili which is around 10 kM away as the crow flies. However, there does not seem to be a direct connection to the airport from that Metro station. It seems as if you have to take either the bus #337 from the 300 Aragveli station or based upon the map, the airport train from the Central Railway Station.
The fares:
1 GEL ≅ $0.50 = 90 min (including transfers)
3 GEL ≅ $1.50 = 1 Day
20 GEL ≅ $10.00 = 1 Week
40 GEL ≅ $20.00 = 1 Month
As far as the website is concerned the reloadable Metro Money card is valued at 2 GEL ≅ $1.00. The Metro Money card I presume is very similar to the Peggo, Presto, Easy GO and the Compass Card.
There are 23 stations in total:
Varketili — Underground — Island Platform — Redline (Terminus)
Samgori — Underground — Island Platform — Redline
Isani — Underground — Island Platform — Redline
300 Aragveli — Underground — Island Platform — Redline — Airport
Avlabari — Underground — Island Platform — Redline
Liberty Square — Underground — Island Platform — Redline
Rustaveli — Underground — Island Platform — Redline
Marjanishvili — Underground — Island Platform — Redline
Station Square — Underground — Redline and Greenline
Nadzaladevi — Underground — Island Platform — Redline
Gotsiridze — Aboveground — Side Platform — Redline
Didube — Ground — Island Platform — Redline
Grmagele — Underground — Island — Redline
Guramishvili — Underground — Island — Redline
Sarajishvili — Underground — Island — Redline
Akhmetlis Teatri — Underground — Island — Redline (Terminus)
Station Square (2) — Underground — Island — Greenline
Tsereteli — Underground — Island — Greenline
Technical University — Underground — Island — Greenline
Medical University — Underground — Island — Greenline
Delisi — Underground — Island — Greenline
Vazha Pshavela — Underground — Island — Greenline
State University — Underground — Island — Greenline (Terminus)
Almost all the stations are underground with the exception of 2 where one of them appears to be elevated and the other at ground level.