Mediterranean

Egypt
Various artifacts from Egyptian tombs, as old as 2500 BC, provide evidence that football-like games existed in that region and time period. On the right, we see a linen ball found in an Egyptian tomb. For better bouncing, balls were also made out of catgut (animal sinew) wound into a sphere and wrapped in leather or deerskin. Little is known about the Egyptian ball games. Historians believe that during fertility rites in Ancient Egypt, balls of seeds wrapped in colorful cloth were booted across the fields.

Episkyros (Greece)
Around 2000 BC, The Greeks developed a kicking/throwing game, called Episkyros (also known as Phaininda.) It was played primarily by men but women also practiced it. Regardless of their gender, the Greeks usually played nude. This marble relief from the National Museum of Archeology in Athens shows a Greek athlete balancing a ball on his thigh, supposedly demonstrating a training technique to the boy. This very same image is nowadays featured on the European Cup trophy. The ball seen in the relief is clearly a "follis" or an inflated ball. Early balls were made of linen and hair wrapped in string and sewn together. They wouldn't have bounced well. Later Greek models like the Follis were made from inflated pig bladders wrapped tight in leather (pigskin or deerskin.) Another technique used for ball-making was chopping sponges and wrapping them in string and cloth.
The Greek game of Episkyros was later adopted by the Romans, who renamed and transformed it into Harpastum.

Harpastum (The Roman Empire)
Harpastum (meaning "the small ball game") remained popular for 700-800 years and was played with a relatively smaller and harder ball, compared to follis or paganica. Harpastum was played by 5-12 players on a rectangular field marked by boundary lines and split by a center line. Each team had to keep the ball in their own half for as song as they can, while their opponents tried to steal it and get it over to their own side. An important rule of Harpastum stated that only the player with the ball could be tackled. That limitation caused the development of complex passing combinations. Players developed specific team roles and a lot of trickery and tactics were probably involved. The feet were scarcely used in the game of Harpastum, but a striking resemblance to rugby can be noted. Emperor Julius Caesar (who is speculated to have played himself) used Harpastum to maintain the physical fitness of his soldiers and keep them battle ready. It is also believed that the Romans took Harpastum to the British Isles at the time of their expansion. By their arrival, less-sophisticated kicking games were already present on the British Isles. There actually are records of a Harpastum match played between the Romans and the British natives. Even although the conquerors won, Harpastum eventually faded out and it is very unlikely that it could have impacted the later development of English mob football.

This is a Roman mosaic is from Ostia. It presents what appears to be an infalted "pila", stitched in the fashion of modern balls. Considering that this scene represents a gym, it might be also a "paganica" or medicine ball. There are historical references of Roman boys playing ball in the streets. Cicero described one court case in which a man getting a shave was killed when a ball was kicked at the barber.

Atheneaus wrote this about Harpastum:

Harpastum, which used to be called Phaininda, is the game I like most of all. Great are the exertion and fatigue attendant upon contests of ball-playing and violent twisting and turning of the neck. Hence Antiphanes, "Damn it, what a pain in the neck I've got." He describes the game thus: "He seized the ball and passed it to a team-mate while dodging another and laughing. He pushed it out of the way of another. Another fellow player he raised to his feet. All the while the crowd resounded with shouts of Out of bounds, Too far, Right beside him, Over his head, On the ground, Up in the air, Too short, Pass it back in the scrum.