What is the Gemara?

The Gemara is the discussion of the Sages on the Mishnah. The Mishnah states the law briefly; the Gemara asks, challenges, brings proofs and clarifies the reasons. Together they are called the Talmud.

Who compiled it?

The Mishnah was edited by Rabbi Yehudah HaNasi around 200 CE. The Babylonian Talmud was sealed in Babylonia in the generations of Rav Ashi and Ravina, around 500 CE. There is also a Jerusalem Talmud, edited in the Land of Israel.

In what language?

The Mishnah is written in rabbinic Hebrew. The Gemara is mostly in Babylonian Aramaic, with Hebrew quotations. Learn a few dozen fixed words and phrases and you already understand much of the page.