Ancient Greek wrestling grounds
The palaestra at Olympia (Greek παλαίστρ-α, -αι, "wrestling ground or grounds," Latin palaestr-a, -ae, with Greek ἐν Όλυμπία, Latin in Olympia) is the ground or grounds in ancient Olympia where πάλη, Doric πάλα, "wrestling," was taught and performed for training purposes; i.e., "wrestling-school." Two other martial arts were taught there: Greek πυγμή (pygme), Latin pugnus, "fist, boxing," and Greek παγκράτιον, Latin pancration or pancratium, "any method," which was free-style, or hand-to-hand, including grappling, kicking, punching, or any unarmed method whatever, no holds barred. The latter was sometimes deadly, or disfiguring (with permission), which indicates that the arts were ephebic, or "soldier" training for prospective citizens of the city-state sponsoring the school, such as Elis, but here combined with prospective candidacy for contention in the games. Be that as it may, none of the games were conducted without rules, umpires, and judges, who did not hesitate to stop contests, fine contenders with in some cases amounts prohibiting future participation, or bar flagrant violators.
The architecture of the martial arts school was standard in the Graeco-Roman world: a hollow square bordered all around by a peribolos ("border"), here a roofed portico, which in turn was bordered by rooms looking inward, and another border outside of it consisting of rooms facing outward, back-to-back with the inner rooms. The outer rooms possibly housed the resident population of athletes-in-training. The layout is standard military similar to that of a camp hospital, which placed patients in the outer rooms and grew medicinal herbs in the quadrangle.
Location.
The ultimate authority on the features of ancient Olympia is generally considered to be Pausanias, who lived and wrote under the "good emperors" in the 2nd century; that is, he was least subject to imperial ideological terror. His "Description of Greek" covers his first-hand observations recorded during his expeditionary travels, Olympia being described under Elis, Books 5 and 6. Two passages are especially relevant to the athletic training school:
The Town Hall (prytaneion) of the Eleans is within the Atlantis, and it has been destroyed beside the exit beyond the gymnasium. In this gymnasium are the running-tracks (dromoi) and the wrestling-grounds (palaistrai) for the athletes.
In the gymnasium at Olympia it is customary for pentathletes (pentathloi) and runners (dromeis) to practise, ... There is also another enclosure (peribolos), less than this, to the left of the entrance to the gymnasium, and the athletes have their wrestling-schools (palaistrai) here. Adjoining the wall of the eastern porch of the gymnasium are the dwellings (oikeiseis) of the athletes, turned towards the southwest.
These passages made it possible for the archaeologists to connect the descriptions of Pausanias to edifices and areas of the excavated site. The "exit beyond the gymnasium" has to be either the north exit, leading to the town, or the south exit, leading (at that time) across the Alfeios River. The gymnasion contains dromoi, but the main running course, the stadium, is not near either exit or any building that could be construed to have been a prytaneum. The only other dromoi found are in item 20, near the north exit. The prytaneum then falls into place as item 2.
Pausanias says that the gymnasion included both the dromoi and the palaistrai, and that both dromeis and pentathloi trained there. The pentathlon was a "five-contest" event: long jumping, javelin throwing, disk throwing, short running, and wrestling. Unless Pausanias repeated himself, the dromeis must have been long-race runners, which fact would leave the stadium with no purpose, unless the gymnasion were only for training. The show was held in the stadium.
The palaistra, reserved for "confrontative," or martial arts, was on the left of the entrance to the gymnasion, which must therefore have been the passageway between items 20 and 21, which led through an entrance building. Entrants could then turn left to the palaistrai or right to the dromoi, an area dubbed the gymnasion by the archaeologists for convenience. Both sides were the gymnasion, a name which was sometimes applied also just to the palaistra. Along the eastern side of the dromoi was another roofed portico (stoa) and along its eastern edge more foundations and rubble. This alone could have been the remains of the oikeiseis, or the term might also include the same sort of remains on the east of the palaistra. At this point Pausanias becomes enigmatic, mentioning the oikeiseis that "turned to the southwest," one possibility being that they continued around to the south side of the palaistra.
Pausanias uses both dromoi and palaistrai, plurals. The Greek possibly uses the plural to mean singular in the case of palaistrai, paralleled by English wrestling-grounds for one ground. This may be true for dromoi, but such a view is archaeologically suspicious. The archaeological gymnasion has a south stoa that runs into the brush on the left bank of the Kladieos.
Evidence acquired after 3000 suggests that there was another dromos approximately in the current bed of the river, which is also believed to have been its original, natural location. A water retaining wall termed "the Kladieos Wall" has been found on the right bank of the Kladieos, suggesting that it was once on the left bank, and was for the purpose of rerouting the river to the west, so that the gymnasion could be built into its former location. The wall is classical, but not precisely dateable. When it was no longer maintained the Kladeos broke into its old channel from the north and washed away the western dromos. Most of the wall remains buried, along, no doubt, with foundations of the western portico, now so far below the water table (like the hippodrome) as to be unexcavateable.
Architecture.
The question of type.
The palaestra is very nearly square, missing it but slightly. The length and width are 66.35 m and 66.75 m, with a difference of . The hollow square, however, is square to . Given the tradition of square palaestras, it is safe to say the palaistra was intended to be square by its builders. The square is oriented with its sides approximately perpendicular to the cardinal points (N, S, E, W). However, it missed that orientation by a 2-degree CCW rotation. Some of the features in the plan have the same offset, some have more of an offset, and a few are aligned on the cardinal points. They all seem aligned on something else; i.e., the rotations are not randomly distributed. As they are of different ages, one might conjecture that the builders of each age were capable of better surveying precision and did have a plan in mind.
The tradition that the palaistra was a type of building was already extant in Greek culture before Pausanias. An ideal type was presented by Vitruvius, Roman architect, in "De architectura" ("On Architecture"), Book 5.11.1 – 5.11.4, although at that time he admitted palaestrae were "not usual in Italy." He thought it best, he said, "to set forth the traditional way," which he believed was Greek. There are certain problems with its credibility. One might well question whether he had actually built any to ideal specifications, or if this is an imaginary model from which to select real features.
Vitruvius constructs a definition of a palaestra, beginning with “a square or oblong peristyle” (peristylia quadrata sive oblonga), which was the preferred plan for any large-area building, as it kept the roof to a minimum and distributed natural daylight to each room. The square shape of the Olympian palaistra caused a mistaken trend in the classical archaeology of the times to identify any square peristyle as a palaistra. After listing several examples, such as a peristyle room in the building at Paestum dubbed “the asclepion of Paestum,” which turned out on later assessment to have been a dining hall, Emme presents five palaistral plans besides Olympia of which he is certain.
These six plans (including Olympia) form Emme's base for defining his palaestral type. Four of them are square, one oblong (Amphipolis). Four are aligned with the sides perpendicular to the cardinal direction, one (Delos) with the diagonals perpendicular; i.e., N-S runs from corner to corner. They date from the 4th to the 2nd centuries BC. However, mere quadrature and directionality are insufficient to distinguish the palaistra, as many other buildings have those. Emme goes on to borrow a page from Vitruvius.
Vitruvius begins his description of the palaestra with some fundamentally wrong assumptions, which demonstrate that he had no first-hand acquaintance with palaestrae. He describes a two-part gymnasion (like Olympia): “inside a palaestra” (5.11.1, 5.11.2), and “on the outside” (5.11.3). Both are apparently squares of colonnades, back-to back in the center. Since they each have a south side, they are aligned N-S. The walkways are called xysti (Greek xystoi), “polished,” (or secondarily "chipped") from the pavements, either glossy or evidencing embedded fragments (tile or concrete with embedded pebbles or rubble). In the northern square the walkways are 10 feet wide. Outside the east and west after a step-down of 1.5 feet are parallel running tracks, unpolished, 12 feet wide. Inside the square a sort of garden is laid out with walks called xysta or paradromides and plantings of plane trees. The whole idea is that in the summer the athletes use the walkways in the center but in winter move to the porticos. The north side is a stadium where contests are held observed by onlookers occupying seats along the north.
It is the dimensions that give Vitruvius away. The periphery of each square must be one diaulos (“two-pipe”), the length of the Olympic stadium and back, the distance of the long run in the games, which, by measurement of the stadium, is double 212.54 or . One side of one square is half a Greek stadion. To complete the long run in the gymnasion the athlete must run around the periphery of the inside track. If he is running on the xystus he must leave it to cross the north side, being exposed to bad weather anyway. Furthermore, the stadium on the north side is only half the Olympic length, too small. The palaestra, however, is bursting with more space than it can ever use. No archaeological palaistrai are that large; most are smaller than the Olympic palaistra, which is dwarfed by its large gymnasion.
The enigma of the rooms.
As a final incongruity Vitruvius describes some 11 different types of rooms around the periphery of the palaestra, 10 of which are across the north side, while the remaining type is duplicated around the other three sides: 5 on the east, 4 on the west, and 2 on the south. Considering that this is a wrestling school, one might reason that these rooms had to do with the teaching of wrestling, but not so. In Vitruvius they are 
…roomy recesses … with seats in them, where philosophers, rhetoricians, and others who delight in learning may sit and converse,
apparently untroubled by all the wrestling being conducted feet from them. These philosophers of the palaistra are similar to the general peripatetic population who might be wandering about the xysta, and are prevented from interfering with the runners by the step-downs, at least in winter.
As for the function rooms across the north, the Olympic palaestra's north side, which is long, is distributed into only 5 rooms, half the required number. The average length per room is , which indicates that the rooms are for groups, not individuals, in contrast to the housing units on the outside the wall. Noting that different palaistrai have different numbers of function rooms, and that most of Vitruvius' rooms remain otherwise unknown, Emme completes his definition of a palaistra by adding the minimum number of known archaeological features possessed by his basic set of palaistrai. They are known from inscriptions, such as those at Delos, and their readily identifiable archaeological characteristics.
Water at Olympia.
Every palaestra must have water for washing. The Romans were lavish in their provision of it, for which their civilization has long been known. They typically provided it in public baths, where for a small price any citizen could anoint himself with oil, scrape it off with the dirt using a strigil, sweat in the heated steam room, wash in hot water, take a cold plunge in the cold room, and spend as much time as he had lounging in the swimming pool enjoying the company of fellow citizens, many of whom were nude women taking a dip.