The question at the heart of the F.B.I.’s Russia investigation is, as the former F.B.I. director James Comey testified earlier this year, “investigating the nature of any links between individuals associated with the Trump campaign and the Russian government and whether there was any coordination between the campaign and Russia’s efforts.” The shorthand used by the news media for this linkage is “collusion.” The guilty plea and criminal indictments unveiled by Robert Mueller, the special counsel, on Monday do not prove collusion. But they provide evidence that more members of Donald Trump’s Presidential campaign, the foreign-policy adviser George Papadopoulos and at least one of his superiors, were at the very least eager to collude with the Russian government. And they also provide evidence that Paul Manafort, Trump’s former campaign chairman, for years tried to influence American politics on behalf of pro-Russia entities in Ukraine without properly reporting his lobbying to the Justice Department.

The surprise news of the morning came when the government unsealed a guilty plea entered by Papadopoulos, one of Trump’s earliest foreign-policy advisers. Papadopoulos had admitted to lying to the F.B.I. about his relationship with a London-based professor who “claimed to have substantial connections with Russian government officials” and promised “dirt” on Hillary Clinton in the form of “thousands of emails.” (The professor was identified by the Washington Post as Joseph Mifsud, the director of the London Academy of Diplomacy.) Papadopoulos also made false statements to the F.B.I. about a “female Russian national” who had links to Russian government officials, and who unsuccessfully worked with him to arrange meetings between the Trump campaign and the Kremlin.

According to the details of the plea, Papadopoulos learned that he would be a Trump adviser in March, 2016. At the time, Trump had few big-name foreign-policy advisers and he was desperate for anyone who could lend credentials to his team, which explains why obscure figures like Papadopoulos and Carter Page were able to join the campaign’s upper ranks of policy advisers. During an editorial board meeting that month at the Washington Post, Trump touted Papadopoulos as an “excellent guy.” (At the time, Papadopoulos was being mocked by reporters because one of the few credentials on his LinkedIn profile was that he had participated in a Model U.N.) The professor mentioned in the indictment, whose name and nationality were not included in the court filing, seems very much like someone either trying to recruit Papadopoulos or at least trying to leverage his connection to Trump’s orbit for the Russian government’s advantage. The professor had only taken an interest in Papadopoulos, who was then living in London, after he knew that he would be an adviser to Trump.

This is the second example of the Trump campaign welcoming an offer from a purported Russian official to work together in an attempt to politically damage Hillary Clinton. Donald Trump, Jr., set up a meeting with a Russian lawyer who also claimed to have information from Russian government officials that would damage Clinton.

In the plea agreement unsealed on Monday, the U.S. government says Papadopoulos believed that his own close ties to the Russian government would boost his standing inside the Trump campaign, not weaken it. The agreement says that Papadopoulos valued the relationship because the professor’s connections to Russian officials “could increase his importance as a policy adviser.” Papadopoulos met with the professor and the woman, who he erroneously believed was Putin’s niece, and reported back to the Trump campaign. His supervisor on the campaign, who is not named in the court filing, made no promises about a broader meeting between the Russians and the Trump campaign, but gave an encouraging nod to his work cultivating Russian sources: “Great work.”

On March 31st, Papadopoulos met in a small group with Trump and other advisers, and seemed to brag that he had Russian connections and that he could arrange a meeting between Putin and Trump. There’s nothing in the plea agreement about how Trump responded. Through the spring, Papadopoulos continued to communicate via Skype and e-mail with his two Russian intermediaries about various potential meetings between the Trump campaign and Russian officials. In April, he got some big news. The professor told him that he had just met with senior Russian officials and that the Russians had “thousands of emails” about Clinton. The document does not explain what these e-mails are, but, according to the intelligence community’s report about Russian interference in the 2016 election, the e-mails of John Podesta, Clinton’s campaign chairman, were hacked by the Russians in March.

With encouragement from the Trump campaign, Papadopoulos continued talking to the Russians through August, 2016. When he was interviewed by the F.B.I. in January, 2017, he lied to them regarding numerous details about his contacts. In July, he was arrested as he stepped off a plane at Dulles International Airport, and in early October he entered the guilty plea. What he was doing between his arrest in July and the unsealing of the guilty plea on Monday is a mystery, but one filing in the case says that the government wanted the plea agreement sealed because agents didn’t want to tip off other targets of the investigation to the fact that Papadopoulos had become a coöperating witness.

The other major developments of the day, the indictments of Manafort and his former associate, Rick Gates, also do not provide direct evidence of collusion. But, for a decade, Manafort and Gates allegedly tried to influence American politics on behalf of a foreign government, Ukraine, without informing U.S. officials. The two men have been charged with conspiracy, money laundering, failing to file required financial reports to the government, acting as unregistered agents of a foreign power, and making false statements.

Some of these alleged crimes continued through 2017, which means they included the period when both men worked for the Trump campaign, but it’s fair to say that the core of their alleged crimes relates to acts that predate Trump: they are accused of spending years stashing money from foreign work in unreported offshore accounts, and laundering it in the U.S. through real-estate deals and other schemes. In addition, they did work in the United States on behalf of their pro-Russian, Ukrainian benefactors without properly registering with the Justice Department, as is required by law. When the F.B.I. came after them, Manafort allegedly lied. Indeed, the reason for the raid on Manafort’s home, in July, is finally clear: he told the F.B.I. that he didn’t have many e-mails related to the foreign lobbying. The F.B.I. didn’t buy it. Agents searched his home and found out that he wasn’t telling the truth.

Trump looked at these charges on Monday and had a predictable reaction. “Sorry, but this is years ago, before Paul Manafort was part of the Trump campaign,” Trump tweeted. “But why aren’t Crooked Hillary & the Dems the focus?????” He added, “....Also, there is NO COLLUSION!”

To a certain extent, he is correct. Mueller didn’t claim that Manafort and Gates colluded with Russia. But the gist of the indictment is that Manafort and Gates were unregistered agents who worked on behalf of pro-Russian entities, from 2006 to 2016, and “directed a campaign to lobby United States officials on behalf of the Government of Ukraine, the President of Ukraine, and Ukrainian political partners.” Before Monday’s indictments, their failure to register as foreign agents seemed like a minor crime. Many legal observers noted that lobbyists can often register with the Justice Department after the fact and spare themselves any criminal liability. But Mueller alleges that the lack of registration was critical to the over-all money laundering and the “multi-million dollar lobbying campaign” in the U.S. that was conducted “at the direction” of Viktor Yanukovych, the pro-Putin President of Ukraine. In other words, they are accused of collusion with a foreign government.

What’s important about this, of course, is that if Manafort and Gates spent years and millions of dollars secretly trying to influence U.S. politics on behalf of Russian interests, it would not be a great leap to believe that they were part of a similar campaign while working for Trump. They allegedly spent a long time practicing.

Like so many other contacts between Trump associates and the Russians, there is no smoking gun in either the Papadopoulos plea agreement or the Manafort and Gates indictments concerning outright coördination between the Trump campaign and the Russians. But, as with previous disclosures concerning Carter Page, Donald Trump, Jr., and Jared Kushner, the Russians found that, when it came to gaining access to top Trump officials, they were often pushing on an open door.