Shiur (//, Hebrew: שיעור [ʃiˈʔuʁ], lit. amount, pl. shiurim שיעורים [ʃiʔuˈʁim]) is a lecture on any Torah topic, such as Gemara, Mishnah, Halakha (Jewish law), Tanakh (Bible), etc.
The Hebrew term שיעור designated amount came to refer to a portion of Judaic text arranged for study on a particular occasion, such as a yartzeit, the dedication of a new home, or the evening of a holiday, and then to a public reading and explanation of the same. The act of teaching and studying these texts at the designated time was known as schiur lernen in Yiddish. These shiurim would be attended by all classes of people; it was traditional for learned attendees to engage the lecturer in continuous discussion, and for the larger lay audience to listen intently.
Concurrently, the word came to refer to the daily study quotient for students of a yeshiva, and then to the lecture given thereon. Akiva Eger, for example,
would not miss learning a single shiur with the yeshiva. His shiurim with them were always three per day: there was a session of Talmud and Tosafot, a session of exhaustive Halakha, and a session of Shulchan Aruch and Magen Avraham, and these were aside from the session of Tur and SA Yoreh De'ah he would learn with his children and some students, and with these he would learn a further shiur of exhaustive Talmud and Tosafot at night.
Shiur may refer to the type of learning that takes place in yeshivot and kollelim, in which students hear an in-depth lecture on the sugya (Gemara topic) the yeshiva is studying at the time.
Typically, yeshiva students attend a daily shiur yomi (daily lecture) given by a maggid shiur (literally, "sayer of the shiur") and a weekly shiur klali (comprehensive lecture, which sums up the week's learning) given by the rosh yeshiva. The rosh yeshiva usually also gives the senior shiur - see below - on a daily basis.
Before the shiur, a bibliography and a series of textual references, or mar'e mekomot,   are posted so that students may prepare for the lecture in advance. Students typically spend several hours preparing for the shiur yomi. After the shiur, students spend additional time reviewing and clarifying the lesson that they have just heard. These preparation and review periods take place in a special time period called a seder, in which students study the lesson individually and/or in chavrutot (study pairs).
Shiurim may also be offered in yeshiva on topics in mussar, Chumash, and hashkafah (Jewish philosophy), depending on the yeshiva and the learning level of its students. The shiur is likewise the typical format for classes at women's seminaries and midrashot.
A shiur is also the name given to the different class-levels in a yeshiva. For example, first-year students are said to be in "Shiur Aleph"; second-year students are in "Shiur Bet"; third-year students are in "Shiur Gimmel, etc. In kollelim, the higher shiurim accommodate more advanced levels of learning. See Yeshiva #Talmud study.
Synagogue rabbis and noted rabbis in the community also give shiurim to their constituencies. In shuls, the shiur given between the Mincha and Maariv services is usually geared to baalebatim (laymen). Noted rabbis give more in-depth shiurim to attendees on Shabbat or weekday evenings, usually in the local synagogue or beth midrash (study hall).
(Public) shiurim thus range in length and depth: from a short "vort", or "Dvar Torah" ("word (of Torah)", in Yiddish and Hebrew respectively), to a detailed "drasha" ("study", from the Aramaic; see midrash); the former above, baalebatim focused, is a vort, while the latter is a drosha. Especially in Chasidic settings, a less formal - often inspirational - shiur may be termed "sicha" (שיחה, lit. "speech"); see also Maamor and Maamarim (Chabad).
Commonly, the Rosh Yeshiva delivers a weekly shiur on the parashah (weekly Torah portion), exploring a particular question or theme. This is usually in-depth, of an hour in duration, and typically open to the public.
Many yeshivot, midrashot, and "community kollels" host yemei iyun ("days of in-depth learning", sing. yom iyun), where community members study a specific topic. These are often held before religious holidays - especially Pesach and the New Year period - preparing the spiritual and halakhik elements of the upcoming festival.
A "Memorial Shiur" is often given to the entire yeshiva / community on the Yahrzeit of a (founding) Rosh Yeshiva or Rabbi; usually exploring a specific topic of general interest.
"Shiur" may include any kind of Torah lesson — including lectures to children, women, and baalebatim (lay audience), and taped lectures circulated via cassette tape, computer hookup, MP3 or MP4 connection, or call-in telephone lines. Some kiruv organizations advertise "five-minute shiurim" to attract beginning listeners.
Similarly, "Vort" and "Dvar Torah", may in fact refer to any short Torah idea, delivered on various occasions,    and not necessarily by a Rabbi; for example: by the host at his Shabbat table, by the leader before "Benching" (grace after meals), or by a guest at sheva brachot, or at any Seudat mitzvah.