A bagel (Yiddish: בײגל‎ baygl; Polish: bajgiel), also spelled beigel, is a bread product originating in the Jewish communities of Poland. It is traditionally shaped by hand into the form of a ring from yeasted wheat dough, roughly hand-sized, that is first boiled for a short time in water and then baked. The result is a dense, chewy, doughy interior with a browned and sometimes crisp exterior. Bagels are often topped with seeds baked on the outer crust, with the traditional ones being poppy or sesame seeds. Some may have salt sprinkled on their surface, and there are different dough types, such as whole-grain or rye.

Linguist Leo Rosten wrote in The Joys of Yiddishabout the first known mention of the Polish word bajgiel derived from the Yiddish word bagel in the "Community Regulations" of the city of Kraków in 1610, which stated that the food was given as a gift to women in childbirth.

In the 16th and first half of the 17th centuries, the bajgiel became a staple of Polish cuisine and a staple of the Slavic diet generally. Its name derives from the Yiddish word beygal from the German dialect word beugel, meaning "ring" or "bracelet".

Variants of the word beugal are used in Yiddish and in Austrian German to refer to a similar form of sweet-filled pastry (Mohnbeugel (with poppy seeds) and Nussbeugel (with ground nuts), or in southern German dialects (where beuge refers to a pile, e.g., holzbeuge "woodpile"). According to the Merriam-Webster dictionary, 'bagel' derives from the transliteration of the Yiddish 'beygl', which came from the Middle High German 'böugel' or ring, which itself came from 'bouc' (ring) in Old High German, similar to the Old English bēag "ring" and būgan "to bend, bow". Similarly, another etymology in the Webster's New World College Dictionary says that the Middle High German form was derived from the Austrian German beugel, a kind of croissan, and was similar to the German bügel, a stirrup or ring.

In the Brick Lane district and surrounding area of London, bagels (locally spelled "beigels") have been sold since the middle of the 19th century. They were often displayed in the windows of bakeries on vertical wooden dowels, up to a metre in length, on racks.