What language to use in Georgia (the country)? Is English widely spoken?

If you know Russian, use it. Despite the political situation, Georgians are smart and open minded. They may not like the Russian government but they love Russian people and they love the Russian language.

I'm pretty convinced after seven months in Georgia that people learn Russian there for just the same reason foreigners everywhere learn English: it's cool and it's useful.

English is spoken, but I wouldn't say "widely". It's spoken by people aged in their 20s and younger, moreso if they're in a big city and moreso depending on their level of education.

In 2010 the Georgian government made a big push for the country to learn English and has been recruiting thousands of native English speakers, mostly from USA, with the goal of having at least one English teacher in every village.

The result is that young kids speak Georgian, a few English words and phrases they've learned at school, and a few Russian words and phrases they've picked up from friends and relatives. People in their teens and twenties are pretty fluent in both Russian and English with just a Georgian accent in both. People in their forties or older rarely speak any English at all but will speak fluent Russian with an accent. (People in their thirties seem to be a bit of a grey zone between the 20s and 40s age groups).

There are also a considerable number of ethnic Russians of various generations living especially in the cities in Georgia. Plenty of ethnic Armenians and Azeris as well as expats live in Georgia too and communicate between each other in Russian.

• If you know some Russian, use it first. It will actually endear you to Georgians more than English at this point. Taxi drivers know Russian but no English. Restaurants aimed at rich tourists have some English speaking staff but in small authentic restaurants and dukanis only Russian (or Georgian) will be useful.
• Use English when your Russian isn't good enough if the other person knows English.
• Georgians are very very impressed with any foreign travellers who can speak a few words of Georgian. Especially in places few tourists go they will be particularly amazed and delighted.

You can get the basics from searching the Internet for videos. Just knowing the numbers one to ten, "hello", and "thank you" is a reasonable goal. It's much more important to learn the Georgian alphabet, which is nothing like the English or Cyrillic alphabets, and in fact not like any other alphabet. The last time I looked not many of these Internet tutorials went much beyond the basics anyway. You can buy imperfect but usable phrasebooks in Tbilisi.

Some more tips:

• Being fluent in Russian won't prevent you from getting ripped off in the bazari but it will make it a bit easier to haggle. Anywhere except the bazaar prices are marked and fair and where they're not it's easy to haggle by smiling and holding up fingers (-:

• If you visit the Armenian-majority cities, don't try to use Georgian. Stick to Russian or win hearts with a couple of Armenian words.

Yes, in general, Georgians have some issues with Russians. But, at the same time, Russians are still (or perhaps, again) regularly visiting the country as tourists, so it ain't that bad. And if it's obvious you're not Russian (for example due to your limited Russian), you won't easily be taken for one.

Russian is most certainly more widely spoken than English.

Georgian is very hard to learn. It would be a great challenge for you. This is the separate language, having very little common with any other language (with exception of Svan and one other language, both spoken in Georgia). Also the alphabet is not similar to anything else, and I've learned only 2 letters of it.

When it comes to Russian, Russian is widely known in Georgia and is considered the international language, the first to try to communicate with foreigners. Some people know English, but I've not met anyone speaking English and not speaking Russian. Knowledge of Russian will be a great advantage for you. The Georgians will not take you for Russian, if you don't speak Russian really good ;)

It is a good idea to learn some words in Georgian, the Georgians are very happy when someone tries to say something in their language. It would be great if you would learn the numbers and the letters of Georgian alphabet - city names on road signs are written in both Georgian and Latin alphabet, but street names are usually in Georgian only (with a few exceptions of old Russian plates).

Well, Georgians speak Georgian, English (which is becoming 2nd most-common spoken language) and Russian. Older people speak Russian and Georigan only, while the younger generation mostly speaks English and Georgian, but nowadays you can communicate with people there in the English language.