I don't know about Georgia, but Ethiopia has had a powerful central government ruled by a Christian monarch since before Islam originated. Presumably, the kings of Ethiopia were powerful enough to resist being taken over by Muslim empires. It might have also helped that a king of Ethiopia gave shelter to a group of Muslim refugees during Mohammed's time.

Did Islam really only spread to places it could conquer? Which is why India never lose Hinduism?

Islam did not only spread to places via conquest. Malaysia and most parts of Indonesia, for instance, are majority Muslim, but the Muslims there converted due to trade, not conquest. As for India, it was at one time ruled by a Muslim dynasty, the Mughals, hence why there are still many Muslims in India today (despite a lot of them fleeing to Pakistan and Bangladesh post-partition).

After the Arab invasion of Georgia, Maslama ibn Mukhallad al-Ansari, the leader of the invasion forces, was given gifts from Stephen II of Iberia as a sign of surrender. To acknowledge this, Maslama issued a "vow of protection," with following points:

• Georgians would be allowed to stay Christian.

• Georgians would have to pay Jizya, which encompassed one Dinar per family.

• Both sides would have to swear not to change the sizes of families to either avoid or increase the tax.

• Georgian population would have to offer military services to the invading force.

• Georgians that would convert to Islam would be freed of Jizya.

The text itself is actually still around. Here's one of the versions in Arabic.

I wrote an essay recently on the spread of Islam in South Asia- I will post it below this comment. It basically goes more into detail on the influence of Muslim traders and the presence of Mughals and Sufism.

I'm not sure about "surrounded". Georgia's proportionally very large northern border is with Russia - a country definitely not Islamic. Much of its southern border is with Armenia, one of the first Christian nations in the world.

But both Georgia and Armenia look a bit like "outposts" in that regard.

For Ethiopia, there was a pact called the Baqt signed by a Caliph that Muslims would not invade Nubia (North of Ethiopia) so long as they provided tribute and slave soldiers. Hence these areas did not fear an assault from the North.

Ethiopia did, however, have conflicts with threats in the East.

Georgia, which was two separate kingdoms for most of its history, played the Ottoman and Persian Empires against each other for centuries. As Georgia is not a large region, it was not of great importance to either empire, and they preferred to fight each other. Not to say that Georgia was not engaged in wars against both, but it managed to stay around largely because the Turks and Persians fought constantly. It is also worth noting that the two main kingdoms of Georgia (there were other minor states that existed at times) were regarded by the Ottoman and Persian Empires as within their own sphere of influence: Imereti in the west was considered Ottoman, while Kakheti in the east was Persian.

This of course led to the downfall of Georgia. It was unable to keep up with the constant warfare and invasions, which devastated the population, landscape, and economy, and sought protection from the encroaching Russian Empire. The resulting Treaty of Georgievsk in 1783 called for the Russians to support Georgia; in reality they ignored the terms of the treaty and instead simply annexed Georgia; Kakheti was occupied in 1801, while Imereti in 1810.

There aren't many good English books on the history of Georgia, but I will suggest one: Donald Rayfield, Edge of Empires: A History of Georgia (London: Reaktion Books, 2012).