GWEN IFILL: Next, two stories on the changing Middle East.
First, from Cairo, Margaret Warner reports on the most potent political force in Egypt, the Muslim Brotherhood.
MARGARET WARNER: Cairo's Al Farouk Hospital is a busy place, welcoming 800 to 1,000 people a day. It was built more than 20 years ago, not by the government or a private charity, but by the Muslim Brotherhood, Egypt's oldest and most well-established Islamic movement.
The Brotherhood operates 21 such hospitals throughout Egypt, providing modern medical care at subsidized prices.
Local resident Mohamed Ramadan is hugely grateful to his neighborhood's benefactor.
MOHAMED RAMADAN, Egypt (through translator): I come here because I like the way the Brotherhood runs it. There's no stealing or corruption, unlike the hospitals run by the government.
MARGARET WARNER: Now the Muslim Brotherhood, long confined to only social and religious service, could soon become the dominant force in the government.
Since the ouster of President Hosni Mubarak seven months ago, all Islamist movements are free to take part in politics. The Brotherhood quickly formed a political wing, the Freedom and Justice Party, to compete in November's parliamentary elections. Though campaigning is not officially permitted yet, its banners hang throughout Cairo.
But the party is taking it slowly. It has pledged to restrict itself to running in only half of Egypt's districts this time.
ESSAM EL ERIAN, Freedom and Justice Party: We need, as people, concrete majority for building the new democratic era.
MARGARET WARNER: Former Brotherhood official Essam El Erian, now vice president of the party, says the Brotherhood won't try to attain a majority on its own, but he hopes that the wider Democratic Alliance for Egypt, that they have joined, will.
ESSAM EL ERIAN: We are not going to have lonely a majority in the incoming Parliament. But we are aiming and targeting to have more than 30 or 35 seats. And with our alliance, we can achieve majority.
MARGARET WARNER: So why would the Muslim Brotherhood, so much better known, financed and organized than any other group throughout Egypt, put any restriction on itself? The reasons are both practical and strategic.
Analyst and writer Amr Hamzawy says, despite its advantages, the Brotherhood knows its limits and what the country and the world will accept.
AMR HAMZAWY, political analyst: They know quite well that they do not have in terms of calibers and skills enough people to rule Egypt on their own. And they have a clear understanding of the fact that the international environment nor the regional environment can take an Egypt which is dominated by Islamists as of now.
And they have patience. I mean, that movement has been out for 80 years, so they know to be patient when they play politics.
MARGARET WARNER: The Egyptian voters they're trying to appeal to are 90 percent Muslim and 10 percent Coptic Christian. Those most are religiously pious, lifestyles here run the gamut.
A recent rally in Tahrir Square sported women in technicolor head scarves and black abaya, men in everything from T-shirts to full beards, and a Philadelphia Phillies fanatic a long way from the South Side leading prayers.
We heard plenty of concern about the Brotherhood's political advantages over the secular parties and their aims.
NASSER ABDELMOHSIN MOHAMED, accountant (through translator): The only political force that has a real platform or experience is the Brotherhood. So it's really not fair for them to be competing against these other parties, which need to be given a fair chance.
MARGARET WARNER: Forty-year-old mother Inez Ali was worried about the Brotherhood's social agenda.
INEZ ALI, Egypt: This is not the Islamic -- they want to take the country to Iran and to the hell. I don't know where.
MARGARET WARNER: Ridiculous, said the Freedom and Justice Party's El Erian.
ESSAM EL ERIAN: That is the wrong perception. We are not going to impose any model of Islam for the people. Egyptian people are Muslims and Christians and religious and obeying and obedient for their faithful beliefs without any compulsory power.
MARGARET WARNER: That may be El Erian's own view, says analyst Hamzawy, but other Brotherhood members do want government to enforce the Islamic code of Sharia more strictly.
AMR HAMZAWY: Where there are tensions, where there are disagreements within the movement and between the movement and its constituencies, its crowd out there in Egyptian society, is with regard to Sharia, the place of Sharia in Egyptian politics. Are they going to be happy with the reference which we have had before, principles of Sharia as Islamic law represent the major source of legislation, or are they going to push for an implementation, a full-fledged implementation of Sharia?
MARGARET WARNER: Though the Brotherhood stuck together during 90 years of repression, now other splits are emerging.
Abdel Moneim Aboul Fotouh, for decades a top Brotherhood figure, was expelled early this summer for defying the movement's decision not to enter the presidential election to come. He thinks the extent of Sharia influence in Egypt now is just fine.
ABDEL MONEIM ABOUL FOTOUH, presidential candidate (through translator): I don't think that there is a lot to change. We're going to turn Egypt into an Islamic state? This is extremist talk.
MARGARET WARNER: Why is that extremist talk?
ABDEL MONEIM ABOUL FOTOUH (through translator): What the extremist group say now is that Egypt wasn't Islamic and it's time to turn to Islam again. And I disagree with that. I believe that Islamic civilization came after the Coptic Christian civilization and, before that, the pharaohs. The Egyptian people are tolerant and accept others. So we are not remaking Egypt. What we want to do is fix it.
MARGARET WARNER: Though the presidential election is after the November parliamentary one, Fotouh's aides are already drawing up a campaign for the digital age. He has more than a dozen offices countrywide and thousands of volunteers, some ex-Brotherhood.
But former colleague El Erian dismisses the threat posed by this split.
Do you think there's any difference between the so-called old guard of the Muslim Brotherhood in terms of your vision of the new Egypt and the -- quote -- "new guard"?
ESSAM EL ERIAN: I am old?
ESSAM EL ERIAN: Am I old?
ESSAM EL ERIAN: When the people know the real perception about Muslim Brotherhood, they will discover that the majority of the group are under 30 years old.
MARGARET WARNER: One thing Aboul Fotouh and El Erian do agree on, the really hard-line Islamic agenda is being pushed by the fundamentalist Salafist movement.
On July 29, millions of conservative Islamists flooded Tahrir Square in a show of force that alarmed many in Egyptian society. Leading the charge were Salafists, whose sect reveres a 7th century interpretation of Islam.
MAHMOUD FATHY, Al Fadila Party (through translator): Salafis aren't calling for a theocracy. We're calling for a civilian Islamic state.
MARGARET WARNER: Thirty-year-old architect Mahmoud Fathy is planning to run from the Salafist party he co-founded, Al Fadila, or Virtue. He says Sharia law eventually should be far more vigorously enforced.
MAHMOUD FATHY (through translator): We're calling for Sharia to be implemented in stages. We'd be mindful of the climate. If people then cross the red lines, then they will be punished.
MARGARET WARNER: And that punishment could include cutting off the hand of a thief.
Do you think, ultimately, that's the best way to protect society from thieves and to prevent people from stealing?
MAHMOUD FATHY: Of course. Of course.
MARGARET WARNER: Would you require women to cover their hair?
MAHMOUD FATHY (through translator): On the veiling of women, we would defer to expert institutions. If they say women should be wearing the veil, then the state will encourage that. And if women say they don't want to wear the veil, then we would ask the institution, what is the punishment?
MARGARET WARNER: El Erian dismisses the Salafist message and prospects.
ESSAM EL ERIAN: Egyptians are moderate people, tolerant people. I think even if other extremists from any side go to the ballots, they cannot win more than 5 percent to 7 percent.
MARGARET WARNER: But analyst Hamzawy isn't so sure.
AMR HAMZAWY: Radical groups, radical interpretations win, especially in moments of uncertainty, of instability. And we are going through moments, a phase of uncertainty and instability in Egypt. Yes, it's not a radical country, but that has very little to do with moderation or lack of moderation in politics. That's a different issue.
MARGARET WARNER: Soon, Egyptians, for the first time in their history, will have the chance to decide how much and in what way Islam will guide their country's future.
GWEN IFILL: In her next story, Margaret profiles three revolutionaries who've found different paths after the spring uprising.