The Republican National Convention this week will offer an opportunity to look at some important questions. One will be how a second Bush administration is likely to shape the country in response to the critical issues of the day.

A second will be how the Republican Party chooses to project itself through the lineup of personalities who will appear and the positions they will take in their speeches. If the GOP hopes to win a majority of votes in the Electoral College in November, the locus of the party will likely be found somewhere between the more moderate positions of figures like former New York Mayor Rudolph Giuliani and California Gov. Arnold Schwarzenegger and the more conservative, flat-earth approaches of Attorney General John Ashcroft and Pennsylvania's own Sen. Rick Santorum.

An important sideshow will be how the Republicans and federal and local authorities deal with the activities of thousands of protesters who plan to be in New York City this week. Wisdom would find the law enforcement people somewhere between letting the demonstrators have their say, in peace, and not letting them trash the convention through disruptive intrusions of informal or formal events. Some protesters may be there not to pursue honest dialogue, but to commit mayhem and violence; we would expect police to respond to such incidents expeditiously and within the law.

A critical part of the proceedings will be what the Republican presidential candidate, George W. Bush, says when he makes his acceptance speech on Thursday. Just as Americans were able to make important judgments about Democratic nominee John F. Kerry when he spoke at his party's convention in July, Mr. Bush's presentation of what he sees as his record and, of greater importance, what he would do in a second term will make for essential viewing.

Here are some of the issues that should be addressed by senior Republicans at the convention, starting with Mr. Bush, on what a Republican administration would seek to achieve with four more years.

1. What next in the Iraq war? The basic problem is the mounting toll of American deaths, the fact that some 135,000 of our forces are tied down, that the agony shows few signs of drawing to an end -- the three-week battle for Najaf is a primary case in point -- and the fact that the United States is pouring out a fortune in Iraq -- an estimated $200 billion so far -- that could be spent more usefully at home.

2. What needs to be done on the economy? Faith that the Bush administration's approach -- cut the taxes of the rich; wait for their tax savings to be reinvested, trickle down and stimulate development; liberate business from constricting regulations -- becomes harder to maintain since over the past three years the country has suffered net job losses of more than 1 million, incurred a record budget deficit, seen the numbers of poor increase and witnessed the gap between rich and poor widen.

3. What are we going to do about skyrocketing medical benefit costs? It has become clear that the climbing cost of health care is a critical factor in the lack of job creation. The projected 8 percent annual growth in this benefit category is causing employers not to hire full-time employees, but to contract out or to seek part-time help.

4. What more is needed on education? "No Child Left Behind" could eventually help, as long as it doesn't simply mean shifting the burden to educate from one part of government to another. But the approach still seems to need important revision: There are too many parts of our school-age population still being left behind.

This will be a very interesting week. There is a lot for the Republicans to talk about.