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Attorney General William Barr has returned Capitol Hill for the first time since his justice department released a redacted version of the Mueller report into 2016 Russian election meddling. Democrats have been waiting impatiently to grill him.

The attorney general spoke to the Senate Judiciary Committee on Wednesday and is due to address the equivalent House committee on Thursday - although there's ongoing dispute over the format of the latter hearing. (Democrats want to have a staff lawyer conduct extended questioning outside of each member's five-minute allotted time.)

Democrats have already revealed several lines of inquiry, and have made clear that even more that might be in store.

Here's a look at some of the questions Democrats have for the Trump appointee.

When did you decide there was no obstruction - and why?

Donald Trump, in an interview last week with Fox News host Sean Hannity, said that Mr Barr made up his mind that the president did not commit obstruction of justice "right on the spot" after receiving the Mueller report.

That cuts against the justice department line that it took several days to review the report and craft the attorney general's four-page letter summarising its findings. It may cause some Democrats to suspect that Mr Barr never actually considered the possibility of presidential obstruction and that an unsolicited June 2018 memo to the justice department about presidential immunity from obstruction charges was indeed an accurate reflection of his views (and quite possibly a prime reason why Mr Trump picked him for the job).

In his four-page summary of the Mueller report, Mr Barr concluded there was "not sufficient" evidence to merit prosecuting Mr Trump because there was no underlying crime of conspiracy with Russia and no evidence of "corrupt intent" by the president.

That was before the Mueller report detailed the long list of possible presidential obstruction, including requests for White House Counsel Don McGahn to fire Mr Mueller and attempts to have then-Attorney General Jeff Sessions resume oversight of the investigation or curtail its scope.

A report by the Washington Post on Tuesday night that Mr Mueller wrote to Mr Barr in late March to complain that his four-page memo "did not fully capture the context, nature, and substance" of the report only raises the stakes.

Expect Democrats to go point by point through these specific instances and press Mr Barr - whenever and wherever they have the chance - to explain why each action didn't meet the threshold for criminal charges.

Did you mischaracterise Mueller's obstruction analysis?

In the obstruction section of his report, Mr Mueller explained that he felt bound by justice department guidelines that prohibited the indictment of a sitting president. Because a president would not be able to present a defence at trial, he reasoned, it would be improper to express a view about whether or not a president had engaged in criminal conduct.

Those, in a nutshell, are the "difficult issues" that the special counsel said prevented his office from making a "traditional prosecutorial judgement". Twice, however, he noted that the report did not exonerate the president.

Mr Barr, in his four-page letter, seemingly glossed over this reasoning, instead saying the Mueller report "sets out evidence on both sides" but, in the end, "did not draw a conclusion - one way or the other". The attorney general then put aside the question of whether a president could be indicted and concluded that the evidence was not sufficient in any case.

Democrats in Congress may challenge Mr Barr's decision to make this determination rather than, say, leaving it to the House of Representatives to review the information as part of an impeachment inquiry.

The attorney general has been pressed to explain why he acted as he did - and why he didn't more clearly explain in the first instance why Mr Mueller left the obstruction issue an open question.

When will it be Mueller's turn?

Watching Mr Barr duck and weave under hostile questions is all well and good, but the man Democrats really want to hear from is the special counsel himself. They'd love to ask him how close the multitude of various contacts Trump campaign officials had with Russians came to criminal conspiracy and how confident he is that various witnesses - including Mr McGahn - are telling the truth.

Tuesday night's Washington Post story about Mr Mueller's dissatisfaction with Mr Barr's summary letter will only make this desire sharper.

Mr Barr will continue to get those questions, too, but his answers have certainly been less than revelatory. If and when Mr Mueller finally steps out of the shadows it will be the kind of high drama seldom seen on Capitol Hill.

For the moment, Mr Mueller is still an employee of the justice department, reporting, ultimately, to Mr Barr himself. The House Judiciary Committee has extended an invitation to the special counsel to appear publicly, and have announced that he will testify later this month. The attorney general could speed the process along, if he wanted to.

At the very least, Democrats still want Mr Barr to explain why he doesn't seem to be much help.

Why all the redactions?

The Mueller report was made public with roughly 36 pages of redacted material. At the time of its release, Mr Barr explained that this action covered four categories of material - dealing with ongoing investigations, grand jury proceedings, sensitive intelligence data and "peripheral third party" information.

For Democrats in Congress, the redacted version - or even a slightly less redacted one - isn't good enough. Democratic House Judiciary Committee Chairman Jerry Nadler has said he wants his committee to see the full report and "underlying evidence".

Expect Mr Nadler and others to press Mr Barr to more fully explain his reasons for withholding the full document from Congress - and provide insight on how the justice department might respond if he receives a congressional subpoena demanding it.

What were the origins of the Russia investigation?

Democrats will get most of the attention during Mr Barr's Capitol Hill appearances this week, but it's worth remembering that Republicans will have just as much time to ask their questions. Expect many of them to try to shift the focus to the early days of the Russia investigation and the now-controversial figures - like FBI Director James Comey, Deputy Director Andre McCabe and Obama administration intelligence officials - who played key roles in what began as a counter-intelligence investigation.

Don't forget about Hillary Clinton either. The probe of her private email server has been mentioned by several Republicans in the Senate during Mr Barr's first-day appearance.

Mr Trump has repeatedly claimed that the Obama White House "spied" on his campaign. While there's no evidence of that, the justice department did obtain a secret warrant to surveil Carter Page, a former foreign policy adviser for the Trump campaign, and used an FBI informant to approach Page, George Papadopoulos - who also advised the Trump team - and Sam Clovis, the campaign's national co-chair.

Several weeks ago, in Senate testimony prior to the Mueller report's release, Mr Barr said that he also believed the government had spied on the Trump campaign.

Republicans will probably encourage the attorney general to expand on his allegations and, perhaps, reveal more about who started the investigation - and why.

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