Timeline: 10,000-4000 BC
Around 10,000 BC, with the end of the last major Ice Age, there began to be a lot more people in the world, and at the same time a global warming period meant that there were fewer good places to live. Things began to get crowded. So people began to live closer together, and we see the first communities and settled cities.
In West Asia and Egypt, people began keeping domesticated animals (mainly sheep at first) by around 7000 BC, and farming wheat and barley and lentils and figs by around 6000 BC. They made beer out of the barley, and they made pottery to drink it in. They began to spin and weave clothes out of flax and hemp and wool. One important site from this time period is the city of Jericho, in modern Palestine.
In Africa, this started out as a time of plenty, with the Sahara a huge grassland instead of a desert. But by 8000 BC, the climate began to get drier, and the desert began to form. North of the Sahara, as in Egypt, people turned to farming wheat. But south of the Sahara, wheat wouldn't grow because the climate wasn't right for it. Gradually the Bantu began domesticating millet, which did grow there.
Further east, in northern India, people began to farm wheat and barley by around 6000 BC. South India may have had the same problem as South Africa, that the same crops that would grow in the north wouldn't grow in the south because of the different environment there.
To the east again, in China, people also began to farm rice and keep animals like pigs and chickens by around 6000 BC. Across the Pacific Ocean in South America and Mexico, people were also, independently, beginning to farm corn and beans and to keep domesticated guinea pigs, by around 5000 BC, and llamas, by about 4000 BC.