This document discusses horizontal curves used in transportation infrastructure to gradually change the direction of roads, railways, and other linear structures. It defines simple, compound, and reverse circular curves used for this purpose. Simple curves are arcs of a circle defined by their radius, while compound curves consist of two simple curves joined together curving in the same direction. Reverse curves curve in opposite directions. Spiral curves with varying radii are also used. The document then provides details on calculating elements of simple circular curves like radius, tangent distance, external distance, middle ordinate, and degree of curvature using standard geometric relationships. It concludes with describing the deflection angle method for laying out horizontal curves in the field using one or two theodolites.