More power for the European parliament, so that it votes on nearly all EU decisions and elects the president of the commission
What about the "f" word?
The word "federal" does not appear in the text, in order to avoid alarming eurosceptics. Instead the document talks about building European ties "in the community way".
The text also says the peoples of Europe are determined to be united in an ever closer fashion and to forge a common destiny.
How will it change my life?
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TIMETABLE
20 June: Draft submitted to EU Thessaloniki summit
Intergovernmental conference agrees final text by spring 2004
May 2004: EU enlarges to 25
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It probably won't, at least not in an everyday sense.
Voters won't notice much difference in the way Europe operates, although the president and foreign minister could in time have very high-profile jobs.
The constitution could also bring some European issues closer to home, as national parliaments vote on whether to try to block specific pieces of European legislation.
And some decisions will be taken in a more transparent way, so people will know how their governments voted on particular decisions.
Who does not like it?
Eurosceptics fear that too much power is being handed to Europe, and that the right of individual countries to block some decisions is being taken away.
There are concerns in some quarters that the role of the president and foreign minister could become too powerful, conflicting with national governments.
And some have questioned whether the new Europe will be any more democratic than the old one, which was renowned for its "democratic deficit".
Why did Europe need a constitution?
The EU will soon have 25 members and its structures need streamlining to prevent paralysis.
The constitution will also replace the EU's series of key treaties passed over the last half a century - a vast collection of papers - with a single document saying what the EU can and cannot do.
It could also give the EU a clearer sense of its purpose, one that the public can easily understand.
The chairman of the Convention that drafted the constitution, former French President Valery Giscard d'Estaing, wants it to be taught in schools.
Most European countries already have their own written constitutions. The UK does not - making it a particularly contentious question for some British voters.
Who wrote it?
Mr Giscard D'Estaing's 108-member convention agonised over the draft for a year and a half.
The members were drawn from EU governments, parliaments and the European Commission.
Reporters said Mr Giscard was visibly moved as the latest draft of the convention was finally approved by the convention in June.
When will the new constitution become law?
If a final version is ready in time, it will be signed in May next year.
Some countries will also hold referendums on whether to ratify it. If any country votes No, there may be a delay while a solution is found.