Yeshiva or yeshivah (Hebrew: ישיבה pl. yeshivot or yeshivos) is an institution for Torah study and the study of Talmud primarily within Orthodox Judaism and primarily attended by males.
Yeshiva is the "generic" name for the entire system of schools that teach Torah, Mishnah and Talmud, to all ages.
A yeshiva for male married students is known as a kollel ("gathering").
Rosh yeshiva (Hebrew: ראש ישיבה) (pl.: Rashei yeshiva, also referred to as "Rosh yeshivas") is a rabbi who is the academic "head", or rosh (ראש), of a yeshiva (ישיבה), a school of higher Talmudic study.
Yeshivas continue the scholarly traditions of the Biblical Sanhedrin and the Seventy Elders (Shivim Z'kenim), wise men [1] (Exodus 24:1,9; Numbers 11:16,24) wherein were discussed and eloborated the 613 Mitzvot (commandments).
Rabbi Chaim was the chief disciple of the famed Elijah of Vilna (1720 - 1797) known as the "Vilna Gaon" (the "Genius from Vilna").