What were Russian goals in trying to provide assistance to Trump's campaign in 2016?

Paul Pillar provides a sober look at Russian goals in their support of Trump's election in 2016 and their continued promotion of his political career in Foreign Interference in U.S. Elections is Even Worse Than You Thought Responsible Statecraft 01/27/2020:

When the interests of the foreign government diverge from those of the United States enough to favor weakening of the United States, the harmful effects of interference multiply. This is the framework for understanding the Russian interference in the 2016 election. It remains unclear how much the original Russian motivation was to discredit American democracy and how much to help elect Trump. Both goals were probably involved, with the emphasis shifting the more Trump’s victory started to look feasible. But viewed from today’s perspective, the two objectives go hand-in-hand.

The incumbent U.S. president is today one of the biggest sources of discrediting American democracy, with his levying of fraudulent charges of voter fraud even after winning an election. On foreign policy matters that would be of most interest to Russia, the Trump presidency has entailed huge disruption to U.S. alliances, to the point of the U.S. president becoming a laughing stock. The last three years have seen a precipitous decline in foreign populations’ trust in the United States. For these and other reasons, Vladimir Putin can conclude that the meddling in the 2016 election was a good investment that has paid him ample dividends. [my emphasis]

A lot of politicians and commentators still seem to be trying to shoehorn Vladimir Putin's Russia into the role vacated by the fall of the Soviet Union in the minds of American policymakers, however dubious some of those views of the USSR were back in the day.

Democratic memes portraying Trump as a Putin puppet are misleading. As Pillar writes, destabilizing the American government to some degree and disrupting American alliances were realistic if ambitious goals to which the Russian government could contribute with their mischief in the 2016 election. It's extremely like that they assumed, like most American pollsters and commentators, that Hillary Clinton would win the 2016 election. They almost surely were aiming at creating distractions for her as President.

Instead, they (and we!) got chaos agent Donald Trump in the White House. It was more than they could have reasonably expected. And Putin's government can't be entirely happy to have such a loose cannon to deal with in the White House.

Pillar also urges more diligence for various kinds of influence, licit and otherwise, that countries like the Arab Emirates, Israel, and Saudi Arabia exert on US foreign policy. He also mentions in passing the issue of foreign government funding foreign policy think tanks. The latter isn't inherently bad. But it means that the terms on which funding is accepted and the source of the funds do need to be considered in evaluating the perspective of think tanks.