Secretary of State Mike Pompeo made his first diplomatic trip to Russia on Tuesday to meet with his counterpart, Foreign Minister Sergey Lavrov, and President Vladimir V. Putin.

The three have a great deal of territory to cover, from many bubbling international conflicts — where Washington and Moscow have often found themselves on opposite sides — to a potential new arms treaty. It is the highest level meeting between American and Russian officials since President Trump met with Mr. Putin in Finland last July.

As the meeting with Mr. Lavrov began, Mr. Pompeo said the discussions were intended to improve ties between the two nations, to “stabilize the relationship,” and to find issues where the two powers had “overlapping interests.”

Here are the issues that are likely to be at the forefront of discussions at the meeting in the Black Sea resort city of Sochi.

Ahead of Mr. Pompeo’s trip, a senior State Department official told reporters that an arms control agreement would be at the top of the agenda.

In February, the Trump administration suspended a landmark nuclear arms-control pact, the Intermediate-Range Nuclear Forces Treaty, also known as the I.N.F., saying the United States would terminate the accord within six months if Russia did not come into compliance with the treaty. The next day, Mr. Putin responded that Russia would also  suspend its obligations.