from Merriam-Webster online: Surveying, function (n)-: a branch of applied mathematics that is concerned with determining the area of any portion of the earth's surface, the lengths and directions of the bounding lines, and the contour of the surface and with accurately delineating the whole on paper.
Then, from Wikepedia we have:
Surveying or land surveying is the technique and science of accurately determining the terrestrial or three-dimensional space position of points and the distances and angles between them. These points are usually on the surface of the Earth, and are often used to establish land maps and boundaries for ownership or governmental purposes. In order to accomplish their objective, surveyors use elements of geometry, engineering, trigonometry, mathematics, physics, and law.
An alternative definition, per the American Congress on Surveying and Mapping (ACSM), is the science and art of making all essential measurements to determine the relative position of points and/or physical and cultural details above, on, or beneath the surface of the Earth, and to depict them in a usable form, or to establish the position of points and/or details.
Furthermore, as alluded to above, a particular type of surveying known as "land surveying" (also per ACSM) is the detailed study or inspection, as by gathering information through observations, measurements in the field, questionnaires, or research of legal instruments, and data analysis in the support of planning, designing, and establishing of property boundaries. It involves the re-establishment of cadastral surveys and land boundaries based on documents of record and historical evidence, as well as certifying surveys (as required by statute or local ordinance) of subdivision plats/maps, registered land surveys, judicial surveys, and space delineation. Land surveying can include associated services such as mapping and related data accumulation, construction layout surveys, precision measurements of length, angle, elevation, area, and volume, as well as horizontal and vertical control surveys, and the analysis and utilization of land survey data.
Surveying (as it relates to Civil Engineering) from Britannica:Online Encyclopedia:
Method of making relatively large-scale, accurate measurements of the earth’s surfaces.
Its principal modern uses are in the fields of transportation, building, land use, and communications. Surveying is divided into the categories of plane surveying (mapping small areas) and geodetic surveying (mapping large areas of the globe). The Romans are said to have used the plane table, which consists of a drawing board mounted on a tripod or other support and a straightedge along which lines are drawn. It was the first device capable of recording or establishing angles. With the publication of logarithmic tables in 1620, portable angle-measuring instruments, called topographic instruments, or theodolites, came into use; they included pivoted arms for sighting and could be used for measuring both horizontal and vertical angles. Two revolutionary 20th-century innovations were photogrammetry (mapping from aerial photographs) and electronic distance measurement, including the use of the laser.