A transit theodolite is a precision instrument used to measure horizontal and vertical angles between visible points. It has several key components including a trivet, foot screws, tri-branch, leveling head, and tripod. A transit theodolite is used for tasks like navigating, surveying, laying out building plans, and measuring angles and straight lines. It has advantages like repeat readings not being needed and providing greater accuracy compared to other theodolites. However, it also has disadvantages such as not being suitable for very accurate work and being inconvenient to transport due to its heaviness.