A theodolite is a precision instrument used to measure horizontal and vertical angles in surveying and construction. It consists of a telescope mounted on a rotating base and vertical axis. The telescope can rotate horizontally and vertically, and is used to view targets. Circular scales on the horizontal and vertical axes precisely measure angles to determine positions, distances, and establish control points. Setting up the theodolite on a tripod and leveling it provides an accurate reference for horizontal and vertical angle measurements to targets.