This monograph presents the first detailed exposition of the formal theory of Branching Space-Times. The theory presented here by Nuel Belnap, Thomas Muller, and Tomasz Placek describes how real possibilities can play out in our spatio-temporal world. In our world, some things that are really possible in Cleveland are not really possible in San Francisco; other things were really possible in 1988 but are not really possible in 2021. The authors develop...