President Carter flew home tonight, no longer quite such a mystery to Western Europe after his first trip abroad since taking office. It could hardly have gone better for him.

The newly elected President was the dominant political figure in Europe these last five days, firmly establishing himself as the leading spokesman not just of the United States but of its allies.

Part of this, of course, was simply because Carter is president of the United States, which Europe looks to for support and military protection. He is expected to dominate.

Part of it was because the President arrived here in a far stronger position politically than any of his counter parts.

Part of it stemmed from the Carter political style - his habit of shaking hands with the bobby outside 10 Dowing Street - which captivated the British press, and presumably its readers.

But beyond all that, it was clear at the end of the trip that Carter came here primarily to win friends and that he was willing to be flexible, to smooth over potential differences, in pursuit of that goal. Where compromise was thought necessary, he compromised, or at least did not press the others to accept his position on some of the touchier issues.

The United States paved the way toward the congenially that marked these meetings with the announcement that it was resuming the sale of enriched uraniun to other nations. It was a gesture, but an important and reassuring one to a Western Europe that depends heavily on imported oil for energy and looks to nuclear power as a way to diminish that dependence.

Amid speculation of a personal feud, Carter met privately with With German Chancellor Helmut Schmidt, and said later that their talk "couldn't have been better." One reason for this, no doubt, was that by then Carter had decided not to press his objections to the West German sale of nuclear power technology and equipment to Brazil.

Carter fears such sales will eventually make it possible for Third World nations to fashion nuclear weapons, and what he accomplished here on the nonproliferation issue was certainly less than he would have preferred. The summit conference agreed to a study of the issue, a small step toward Carter's goal.

It was a typical Carter tactic, the raising of an objection, followed by willingness to back down somewhat in order to gain something. Its closest domestic parallel was Carter's attempt to halt more than 30 water projects he considered wasteful. The president ended up approving a number of the projects, but White House officials believe he set an important precedent and that Congress is less likely now to approve questionable water projects in the future.

Carter deferred to Schmidt on another issue he cares about deeply; human rights. Carter brought the subject up only once, and then briefly, during the summit in difference to Schmidt's strong feeling that any official statementon the subject would have an adverse impact on getting ethnic Germans out of Eastern Europe.

Nor was there an American attempt to set higher rates of economic growth for the stronger-conscious West Germans opposed.

Addressing the meeting of the North Atlantic Treaty Organization ministers here today, Carter went out on his way to reassure Europe about his human rights stand, taking a noticably softer approach than he has at home.

"American's concern for human rights does not reflect a desire to impose our particular political or social arrangments on any county," he said. "It is, rather, an expression of the most deeply felt values of the American people. We want tthe world to know where we stand."

The President added: "We entertain no illusion we take will bring rapid changes in the policies of other governments. But neither do we believe that world opinion is without effect."

The NATO speech, with its assurance that the United States will continue to make NATO "the heart of our foreign policy" and its suggestion of an increase in U.S. purchases of European-made military equipment, was typical of Carter's approach throughout this trip.

In public comments, he deferred to his more experienced counterparts, calling them his seniors and saying, as he so often does, "I have a lot to learn from them."

From all accounts, he made the impresssion he wanted, not only on the public but on the leaders of the other nations. The supposed feud with Schmidt never materialized. French President Valery Giscard d'Estaing invited him to visit France this fall and he accepted.

Today, the leaders of Western Europe's smaller countries beat a path to Carter's door after persuading American officials at the last minute to give them at least a fleeting apportunity - five minutes in the case of Premier Gaston Thorn of Luxembourg - to meet Carter face-to-face.

Tonight, as the President was leaving London, British Prime Minister James Callaghan called him "a breath of fresh air in the Western world."

But for all his personal and political success over the last five days, Carter did not leave Europe for Washington with all the questions answered and all the disputes settled.

It remains unclear, for example, whether the talks here and the followup sessions will result in more caution in the export of nuclear technology to the Thrid World. If not, Carter's backing away from the issue at the summit only postponed a showdown if he is to stick with his nonproliferation stand,

Nor, is it by any means assured, despite all the optimism at the end of the economic talks, that the goals of increasing employment without inflation will be realized.

Finally, Carter has much prestige staked on his attempts to achieve a Middle East peace settlement and his trip to Geneva yesterday to meet Syrian President Hafez' Assad pointed up the importance he places on it. While his talks with Assad were friendly, progress toward a peace settlement remains much in doubt.

The issues, and others remains to be addressed the future. At the very least, however, the President's first venture in personal overseas diplomacy appeared to be an enormous political success.