The 17th Hintze Lecture, given by Professor Rocky Kolb, Arthur Holly Compton Distinguished Service Professor of Astronomy and Astrophysics, The University of Chicago. In daily life we do not experience the quantum nature of the world on the scale of elementary particles, nor do we sense the expansion and evolution of the universe on cosmic scales. Humans, midway in size between quantum and cosmic scales, evolved to perceive nature not as it actually is, but merely as required to survive in our environment. How remarkable that we have developed an understanding of the quantum realm and the cosmic realm, and realized that the inner space of the quantum and the outer space of the cosmos are intimately connected. In this lecture I will highlight some of the remarkable connections between the quantum and the cosmos.