Is the purpose of the rise of radical Islamist taking one city after another to unite by force to form a Islamic transnational state and?

It could be the ultimate aim, which was what the Ba'ath Party was originally all about. There would have to be an enormous religious and political paradigm shift for this to happen, though. Many of the Islamic factions have been warring for centuries. Then there are the general, everyday tribal and political divisions. The current tyrannies, such as Saudi Arabia and Kuwait, would have to acquiesce as well. The changes, although not impossible, are improbable.

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They want to form a caliphate(Islamic nation ruled by Sharia Law).