Hydrogen exchange reaction, H + H?, has been studied for over eighty years, yet our understanding of this simplest neutral chemical reaction is incomplete. Research presented in this book are nature´s answer to the question, ´Where do products of the H + H? reaction scatter with respect to a particular direction in the center-of-mass frame?´. Differential cross sections offer an invaluable insight into the H + H? reaction dynamics. Some of the findings follow our intuition, based on classical mechanics, wherein the collision between a hydrogen atom and a hydrogen molecule could be thought of as a type of molecular billiards. Our naive models of the H + H? reaction fail, when the product kinetic energy becomes small. Although the experimental results can still be interpreted in the realm of classical mechanics, a better way to think of chemical reactions is to picture a warped billiard table that changes its shape as the molecules approach one another. Geometric phase effects in the H...