In the 2-3 centuries following the compilation of the Mishnah more commentaries and legal discussions were written and collected into works called the Gemorah. Two different Gemarah were compiled; one in Babylonia and one in Palestine. Collectively the Mishnah and Gemarah are called the Talmud. While there is overlap between the Babylonian (or Bavli) and Palestinian (or Jerusalem or Yerushalmi) Talmuds, the Babylonian is the larger and more comprehensive work.
The orders are:
Complete sets of the Palestinian/Jerusalem Talmud are generally shelved in BM 498. They are shelved in this order: original language (BM 498), selections (BM 498.2), translations (BM 498.5), early works about the Jerusalem Talmud (BM 498.7), then later works (BM 498.8). Individual orders and tractates are shelved with individual orders and tractates of the Talmud under BM 506
Complete sets of the Babylonian Talmud (also just called Talmud without the Babylonian qualifier) are generally shelved in BM 499. They are shelved in this order: original language (BM 499), selections (BM 499.2), translations (BM 499.5)
Works about the Talmud are shelved in BM 500-BM 504
BM 500-500.5 Collections, concordances, dictionaries, etc.
BM 501 Development of the Talmud: general works, then Soferim, Tannaim, Amoraim, Saboraim, Geonim, Rishonim, Aharonim
BM 502 Talmudists, Talmudic academies, then individual talmudists.
BM 503 Authority, traditions, introductions, methodology, textual criticism.
BM 504 Commentaries
Individual orders and tractates are shelved under BM 506
Note: many of these works are shelved in the oversized (folio) section.
To find texts of the Talmud do a title browse search for: talmud <part> <language>
for example: Talmud english
or: talmud berakhot german
or: talmud zevahim
To find books written about the Talmud, do a subject browse search under: talmud <part>
for example: talmud bezah
Bar Ilan Responsa Project
Includes the Hebrew texts of the Tanakh, Talmuds, early commentaries, and many responsa http://www.responsa.co.il/
More options are available to HUC students and faculty by accessing the Responsa Project through the Jewish Studies Portal
English Babylonian Talmud
This Soncino translation is available in 1or 2 column formats.
The Babylonian Talmud Translated by M.L. Rodkinson 
This abridgement of the Talmud covers Mo'ed and Nezikin only.
Jewish texts at Snunit
Includes the Hebrew texts of the Tanakh, Mishnah, Tosefta, Talmud Bavli, Talmud Yerushalmi, and Mishneh Torah
Talmud at e-Daf.com
This site has images of Talmud pages with audio files in English, Hebrew, and Yiddish.
Moznaim Daf-yomi Talmud at Hebrewbooks.org
This site has images of the Talmud pages in searchable pdf files.
A Page of Talmud
This interactive site features a "map" of a page of Talmud. Scroll down the page and you will see who wrote the commentary with a brief biographical note.
A Page of Talmud
While the Library thinks that these sites are useful, their content is not under our control and may express views that are not shared by the Hebrew Union College-Jewish Institute of Religion.
If you have any further questions about finding information on this, or any other topic, ask your local HUC-JIR librarian or email us using the form on the campus library homepage.