Well the main thing - monotheism became prevalent in most of the world. I see people mentioned Christianity - funny how they forget Islam. Prior to Christianity, I can only think of one religion that believe in one God - Judaism. Judaism spawned both Christianity and Islam (some Muslims may have issues with that but the Jewish faith is recognized in the Koran). So over Europe and the Middle East (and parts of Asia) - monotheism. Monotheism is a huge development as it united different cultures and language into one common belief - quite a powerful tool for those in power. However, there was a lot of religious things that went on - the Council of Nicaea - stuff like that.
The Fall of Rome and the rise of Byzantium. Also, during the first century - modern day Europe slowly started to develop in what it is today. The Franks, under Charlemagne, began to gain momentum in modern day France (that's house France got it's name - Franks). Also, it was the Franks that stopped the growth of Islam in Europe. Had the Franks not been successful in stopping the Moors - there is a good chance much of Europe would be Muslim (although with the mass immigration into Europe today, many would say the Muslims are already firmly in Europe).
During this time something called technology transfer was starting to happen. This when ideas, inventions that were discovered or used in lets say Asia slowly came to Europe. Unfortunately during that time, Europe sort of took a step back in inventions and advancements.
In the Far East gunpowder was invented, Kyoto was invented. At this time period, one could argue that Asia had the most advanced societies. Much of Asia didn't change from this time until 1730 or so. That's a long time to have a stable society -especially in China. Not being an expert in Asian History but from what I've read - the monarchs or families in power, stayed in power for hundreds of years.
Now, I'm not sure if this part of your assignment or relates to your assignment - but Asia was far advanced that Europe. Even the Middle East was more advanced the Europe. You can't call the 1st Century the Dark Ages - that came later on but the late 1st Century wasn't necessarily enlightening time. Europe sort of took a step "backward" after the fall of Rome in terms of hygiene, science and basic living. Algebra was invented by the people of the Middle East and I would guess so was the Arabic number system - which we use today. It was during this era that Latin began to die.
Outside the Church - Latin was not being used. Greek dominated Eastern Europe. From modern day Moscow down to southern Turkey, people spoke Greek in the first century. In Western Europe, the barbarian tribes were being used - and from what we can tell seemed to use Latin at it's base.
So that's what I came up with - have fun.