Faiyum (/faɪˈjuːm/ fy-YOOM; Arabic: الفيوم, romanized: el-Fayyūm, locally [elfæjˈjuːm]) is a city in Middle Egypt. Located 100 kilometres (62 miles) southwest of Cairo, in the Faiyum Oasis, it is the capital of the modern Faiyum Governorate. It is one of Egypt's oldest cities due to its strategic location.

Originally founded by the ancient Egyptians as Shedet, its current name in English is also spelled as Fayum, Faiyum or al-Faiyūm. Faiyum was also previously officially named Madīnat al-Faiyūm (Arabic for The City of Faiyum). The name Faiyum (and its spelling variations) may also refer to the Faiyum Oasis, although it is commonly used by Egyptians today to refer to the city.

The modern name of the city comes from Coptic  ̀Ⲫⲓⲟⲙ /Ⲡⲉⲓⲟⲙ epʰiom/peiom (whence also the personal name Ⲡⲁⲓⲟⲙ payom), meaning the Sea or the Lake, which in turn comes from late Egyptian pꜣ-ym of the same meaning, a reference to the nearby Lake Moeris; the extinct elephant ancestor Phiomia was named after it.

Archaeological evidence has found occupations around the Faiyum dating back to at least the Epipalaeolithic. Middle Holocene occupations of the area are most widely studied on the north shore of Lake Moeris, where Gertrude Caton Thompson and Elinor Wight Gardner did a number of excavations of Epipalaeolithic and Neolithic sites, as well as a general survey of the area. Recently the area has been further investigated by a team from the UCLA/RUG/UOA Fayum Project.

According to Roger S. Bagnall, habitation began in the fifth millennium BC and a settlement was established by the Old Kingdom (c. 2685–2180 BC) called Shedet (Medinet el-Fayyum). It was the most significant centre of the cult of the crocodile god Sobek (borrowed from the Demotic pronunciation as Koine Greek: Σοῦχος Soûkhos, and then into Latin as Suchus). In consequence, the Greeks called it "Crocodile City" (Koine Greek: Κροκοδειλόπολις Krokodeilópolis), which was borrowed into Latin as Crocodīlopolis. The city worshipped a tamed sacred crocodile called, in Koine, Petsuchos, "the Son of Soukhos", that was adorned with gold and gem pendants. The Petsoukhos lived in a special temple pond and was fed by the priests with food provided by visitors. When Petsuchos died, it was replaced by another.

Under the Ptolemaic Kingdom, the city was called Ptolemais Euergétis (Koine Greek: Πτολεμαῒς Εὐεργέτις) until Ptolemy II Philadelphus (309–246 BC) renamed the city Arsinoë and the whole nome after the name of his sister-wife Arsinoe II (316–270 or 268), who was deified after her death as part of the Ptolemaic cult of Alexander the Great, the official religion of the kingdom. Ptolemy II Philadelphus also established a town at the edge of Faiyum named Philadelphia. It was laid out in a regular grid plan to resemble a typical Greek city, with private dwellings, palaces, baths and a theatre.

Under the Roman Empire, Arsinoë became part of the province of Arcadia Aegypti. To distinguish it from other cities of the same name, it was called "Arsinoë in Arcadia".

With the arrival of Christianity, Arsinoë became the seat of a bishopric, a suffragan of Oxyrhynchus, the capital of the province and the metropolitan see. Michel Le Quien gives the names of several bishops of Arsinoë, nearly all of them associated with one heresy or another.