Some sources document its establishment in 1803 whilst others cite 1806. The Yeshiva was known as The Chassam Sofer Yeshiva, or simply as Pressburg Yeshiva. The Pressburg Yeshiva was run as an autonomous institution, without the intervention of the community. Unlike Yeshivas in Czarist Russia which were forced to operate clandestinely, the Pressburg Yeshiva was recognized by the Austro-Hungarian Empire whose emperor Franz Joseph I sympathized and respected the Jews and their leader Rabbi Sofer. The Yeshiva was licensed by the Minister of Education of the Austro-Hungarian Empire. Under the law, the school required the four upper grades to study secular studies. These secular studies were not taught in the yeshiva, but students attended and took exams at another Jewish school in Pressburg run by the orthodox Jewish community. All of the yeshiva's students were exempted from military service; most of the military rabbis who served in the Austro-Hungarian Army were graduates of the Pressburg Yeshiva, and held officers’ ranks. The Yeshiva was founded at the height of the Age of Enlightenment and surge of the Jewish Haskalah movement. As such, the Chassam Sofer stood at the forefront against any reform to traditional Judaism and trained his many students to maintain strict observance of Torah and Shulchan Aruch. This yeshiva produced hundreds of future leaders of Austro-Hungarian Jewry who made great influence on the general traditional orthodox and future Charedi Judaism. Notable students of the Chassam Sofer were:
Upon Moses Sofer's death on October 3, 1839, his son, Rabbi Avraham Shmuel Binyamin succeeded him as Rosh Yeshiva. Like his father, Rabbi Samuel Binyamin was a man of great Talmudic knowledge and of great character. Even the Emperor Franz Joseph, was impressed by him and recognized the Yeshiva as an official theological college. This status exempted students from military service. Amongst his students were:
Rabbi Reuven Chaim Klein Author of Shenos Chaim Chaim.
Upon Rabbi Shmuel Binyamin's death on December 31, 1871, his son, Rabbi Simcha Bunim Sofer assumed both the positions of Rav of Pressburg and rosh yeshiva of the Pressburg Yeshiva which number some 400 students at the time. The Tiferess Shabboss Society was established in 1883 by students of the Pressburg Yeshiva. The society aimed at awakening learning competition between the Yeshiva students. Every Shabbat, one of the young men was chosen to give a "shiur" on the subject being learnt in the yeshiva. In 1903 a booklet was published by the Tiferess Shabboss Society, bearing its own name. This book names some 240 students who were learning at the Pressburg Yeshiva at that time. Amongst the young men mentioned are dozens of Hungarian rabbis, including a few Gedolei Torah : Other known students were:
In 1907, after the passing of Rabbi Simcha Bunim, his son Rabbi Akiva Sofer assumed leadership over the Pressburg Yeshiva and congregation. The First World War and the resultant breakup of the Habsburg Empire brought tumultuous times to the Yeshiva. Pressburg became Bratislava and passed to the dominion of the new country Czechoslovakia. Countries such as Hungary, Austria, Germany and Poland hampered efforts of students trying to reach the Yeshiva with difficulties attaining passports and visas. Nonetheless, the Yeshiva flourished and continued to operate. After the Czech crises of 1938 and Hitler’s invasion of the country, Rabbi Akiva fled Hungary. Upon the advice of his uncle, Rabbi Shimon Sofer of Erlau, he escaped to Switzerland and from there to Jerusalem, where he re-established the yeshiva in the Kiryat Moshe neighborhood. Amongst his students were:
