The rise of Artificial Intelligence (AI) will bring with it an ever-increasing willingness to cede decision-making to machines. But rather than just giving machines the power to make decisions that affect us, we need ways to work cooperatively with AI systems. There is a vital need for research in "AI and Cooperation" that seeks to understand the ways in which systems of AIs and systems of AIs with people can engender cooperative behavior. Trust in AI is also key: trust that is intrinsic and trust that can only be earned over time. Here we use the term "AI" in its broadest sense, as employed by the recent 20-Year Community Roadmap for AI Research (Gil and Selman, 2019), including but certainly not limited to, recent advances in deep learning. With success, cooperation between humans and AIs can build society just as human-human cooperation has. Whether coming from an intrinsic willingness to be helpful, or driven through self-interest, human societies have grown strong and the human species has found success through cooperation. We cooperate "in the small" -- as family units, with neighbors, with co-workers, with strangers -- and "in the large" as a global community that seeks cooperative outcomes around questions of commerce, climate change, and disarmament. Cooperation has evolved in nature also, in cells and among animals. While many cases involving cooperation between humans and AIs will be asymmetric, with the human ultimately in control, AI systems are growing so complex that, even today, it is impossible for the human to fully comprehend their reasoning, recommendations, and actions when functioning simply as passive observers.