Mishna: about 200 CE
Jerusalem Talmud: about 400 CE
Babylonia Talmud: about 500 CE
http://www.jewishvirtuallibrary.org/jsource/Judaism/talmud_&_mishna.html
...During the centuries following Rabbi Judah’s editing of the Mishna, it was studied exhaustively by generation after generation of rabbis. Eventually, some of these rabbis wrote down their discussions and commentaries on the Mishna’s laws in a series of books known as the Talmud. The rabbis of Palestine edited their discussions of the Mishna about the year 400: Their work became known as the Palestinian Talmud (in Hebrew, Talmud Yerushalmi, which literally means “Jerusalem Talmud”).
More than a century later, some of the leading Babylonian rabbis compiled another editing of the discussions on the Mishna. By then, these deliberations had been going on some three hundred years. The Babylon edition was far more extensive than its Palestinian counterpart, so that the Babylonian Talmud (Talmud Bavli) became the most authoritative compilation of the Oral Law. When people speak of studying “the Talmud,” they almost invariably mean the Bavli rather than the Yerushalmi.
The Talmud’s discussions are recorded in a consistent format. A law from the Mishna is cited, which is followed by rabbinic deliberations on its meaning. The Mishna and the rabbinic discussions (known as the Gemara) comprise the Talmud, although in Jewish life the terms Gemara and Talmud usually are used interchangeably.
The rabbis whose views are cited in the Mishna are known as Tanna’im (Aramaic for “teachers”), while the rabbis quoted in the Gemara are known as Amora’im (”explainers” or “interpreters”). Because the Tanna’im lived earlier than the Amora’im, and thus were in closer proximity to Moses and the revelation at Sinai, their teachings are considered more authoritative than those of the Amora’im. For the same reason, Jewish tradition generally regards the teachings of the Amora’im, insofar as they are expounding the Oral Law, as more authoritative than contemporary rabbinic teachings.
In addition to extensive legal discussions (in Hebrew, halakha), the rabbis incorporated into the Talmud guidance on ethical matters, medical advice, historical information, and folklore, which together are known as aggadata.
As a rule, the Gemara’s text starts with a close reading of the Mishna...
The first of the great Amoraim (authors the Gemara) was Yehoshua ben Levi, who is believed to have died in the 270s.
We're talking years here, not centuries.