The Tower of Babel

After The Flood at the Time of Noah, the people on Earth had one and the same language (Gen 11:1). They then decided to build a city and a tower with its top in heaven (Gen 11:4a). The city was called Babel in the land of Shinar (Gen 10:10, 11:2, 9). Nimrod is considered the leader of those who built the Tower of Babel 
(1 Chron 1:10, Gen 10:8–12). The reason for doing this wasn't to honor God.
It was to make a name for themselves and to prevent them from being dispersed around the world (Gen 11:4b). 

This was a direct rebellion against God's Word to Noah. God had told Noah
to be fruitful, multiply, and fill the Earth (Gen 9:1, 7), see this explained at 
The Flood at the Time of Noah. Before that, at the beginning of creation, God had told Adam and Eve to be fruitful, multiply and fill the Earth (Gen 1:28). But the people didn't want to obey God. This can be seen as a kind of extreme nationalism.

See this explained at:

• Time 7:27–10:06 in DAVID GUZIK SERMON ON GENESIS 10-11 . ..
• Time 2:42–5:32 in Revelation 17-18 • "Fallen is Babylon the Great!".
  
• Time 15:08–21:38 in 2 Timothy 3 (Part 1) :1-9 • The World in Last Days.

What we have in our hearts, our attitudes, is of the greatest concern to God. God wants our hearts. God therefore decided to confuse their language so that they wouldn't understand each other (Gen 11:6–7). See chapter The Origin of the language in The Origin of Man. Note that it's the persons of the Trinity who speak to each other (Gen 11:7), see The Trinity. The Lord scattered them from there, over all the Earth, and they stopped building the city. (Gen 11:8–9).

The Minimum Number of People to Build the Tower

At the time of the Tower of Babel, the people lived closely together, with Nimrod
considered as the leader. It was during the time of Peleg that the Earth was divided
(Gen 10:25), that is, the people were scattered. We have the following generations:

• Ham->Cush->Nimrod (Gen 10:6, 8).
• Shem->Arphaxad->Shelah->Eber->Peleg (Gen 10:21–25, 11:10–17).

See at time 13:13–17:37 in Were the pyramids built before the flood? about the
building of the tower. See also Which Version of the Old Testament did Jesus Use?
More people available also meant a shorter construction time for the tower.

See also The Old Testament of the Bible.