My list has only one book because presidents have little time to read entire books. The book is Weapons of Mass Migration by Kelly Greenhill. To be clear, while migration is a huge issue (just as Europe these days), that is not why I would recommend it. Instead, it addresses the central problem facing the United States today: success.
Huh? The US is the most powerful country in the world (not there, China). And it would largely prefer for the status quo to remain. The problem of success is that countries and other actors cannot attack the US conventionally--either via war or trade war. The US is simply too good on the conventional battlefield. So, opponents must try asymmetric strategies and means to thwart the US. We have become most familiar with non-state actors (terrorists, insurgents, hackers) using unconventional efforts to impose costs on the US so that it changes its policies.
But we have not really thought so clearly about how weak countries can develop asymmetric strategies to challenge more powerful countries and this is where Greenhill comes in. Her book focuses on how weaker, non-democratic countries can threaten migration crises to impose costs on the US and other advanced democracies: if the more powerful actors don't give in, the weaker player will force people to flee their country and create a refugee crisis where they land. This puts democracies into a difficult spot since they face a conflict between interests and values--that most democratic leaders don't want to absorb large numbers of refugees (tis costly in dollars and helps to foster xenophobia and thus domestic political challenges) but they don't want to push the refugees back since it mean risking the lives of these unfortunates.
This is not a new dynamic, but Greenhill does a great job of understanding it and, more importantly, opening up our imagination to other ways in which weaker states can try to challenge more powerful ones. Any leader of the US needs to understand this challenge in the 21st century: that American strengths are very good at some things but this will lead to the opponents having to figure out other ways to thwart the US. To be clear, this effort by weaker countries often does not work out too well for them (ask Qaadafi!), but the costs are still generated and imposed upon the US and its friends, which means even failed attempts are a problem.
Anyhow, this book, more so than those on the usual lists, makes me think (and by extension any President because she and I have so much in common) differently about the challenges ahead. And we need more different thinking since the old thinking is good for keeping the US in a good conventional position but not so good at the responses to our conventional strength.