The application of certain design principles relating to the form and use of urban settlements: form is dependent upon mass (buildings, their bulk, modelling, and height, and the land they occupy) and space (e.g. streets and open spaces defined by buildings), and use of both buildings and spaces (whether intensive or not) also plays an important role. Several commentators have agreed that there are five categories of relationships in urban built form: routes (e.g. alleys, streets, canals, etc.); boundaries (e.g. natural or built boundaries, such as water-fronts); districts (e.g. clearly defined residential quarters, central areas, etc.); nodes (e.g. junctions of routes, such as squares, etc.); and landmarks (e.g. built fabric, usually monumental, with significant visual, symbolic, or aesthetic identities). Towns and cities existed in Antiquity. At Ur (present-day Iraq), for example, in the fourth millennium bc, there were routes (alleys and streets), with clearly-defined plots for housing, and important monuments. Settlements laid out on grids (a convenient means of defining land for development) existed in China, Ancient Egypt, Mexico, and Ancient Babylon. In the last, a processional route of considerable magnificence was created. When the Greeks created new cities from scratch (e.g. Miletus, by Hippodamus (C5 bc) ), grids, rationality, and geometry were employed, and theories of urban design evolved whereby social order could be expressed. Many public buildings and monuments were erected in Athens, but these were not related to each other in formal geometrical ways: the creation of vistas, and the exploitation of geometry to create splendid effects in cities were evolved in Hellenistic settlements such as Pergamon (C3 bc), although stupendous formal arrangements of processional ways with symmetrically disposed buildings had been created by the Ancient Egyptians in their great temple complexes at Karnak and elsewhere. Geometry was further exploited by the Romans, who developed Hellenistic themes, and who created huge public buildings (e.g. thermae), fora, circuses, arenas, etc., all treated with great architectural splendour. High-density urban living was possible through the creation of blocks of apartments (see insula) bounded by streets, and buildings for large numbers of spectators were erected (e.g., the Colosseum, Rome). By the standards of Antiquity, Rome was a true metropolis, requiring major engineering works to provide it with water and eliminate its wastes. Its defensive walls alone were major undertakings, and its dead were disposed of in linear cemeteries (e.g. Via Appia Antica), in columbaria, or in catacombs. In short, Ancient Rome was a remarkable example of a sophisticated and well-organized city that was a precedent for many of the world-cities of C19. The Romans also created many new towns, based on the standard castrum plan with two main thoroughfares crossing each other at right angles, a forum in the centre, and public buildings (e.g. thermae, temples, etc.) arranged within the logical grid-plan. Constantinople, too, was a world-city, richly embellished with vast churches and public buildings, and with monuments of considerable cultural resonance.
Islamic cities in Central Asia and elsewhere, with their madrasas, mosques, etc., also had sophisticated architectural responses to commerce, religion, and social interaction (e.g., at Isfahan), while huge mosques (e.g., the Mezquita Aljama, Córdoba, Spain) attest to the importance of geometry and formal axes in the creation of urban monuments. In contrast, urban organization in Western Europe declined after the fall of Rome, and it was not until C12 that some kind of recognizable order in urban design was again apparent in the bastide towns and other settlements in France, England, Spain, and Germany (e.g. Villeneuve-sur-Lot, Flint, etc). Generally speaking, however, medieval European towns and cities were densely developed within their walls, with main routes leading from the gates to the centre, where market places (often containing guild or town halls, and surrounded by houses of the more substantial burghers-e.g. Brugge, Antwerp, Brussels) and large churches were built. In Flanders especially, the magnificent Gothic guild and town halls attest to the wealth and power of commerce, and in Northern Italy too, civic aspirations created noble spaces and buildings, as in Siena and Florence.