The Tower of Babel - isn't unity good?

Parshat Noach: What happened with the Tower of Babel? What did they try to achieve, and why were they punished by being dispersed?

Tuvia and Yitzi ,

Tower of Babel
Tower of Babel

This week we read about מגדל בבל, the story of the Tower of Babel. What exactly happened there? What did they try to achieve and why was their punishment to be dispersed into different nations all over the world?