How has the Talmud had an influence on Jewish history?

How has the Talmud had an influence on the next 1,000 years of Jewish history and why?

The Talmud has been the core source of Jewish knowledge for two thousand years. When the Rabbis have a question of how to apply the Bible to modern times, they must base their conclusion on precedent that had its sources in the Talmud. Today Jewish Law had been codified in a book that is called the Shulchan Aruch.

Ok, but the way I see the Talmud is a tradition book handed down. The Mezuzah, a mild detail. How many sabbath commandments in the talmud?

All the 613 commandments are discussed in the Talmud. The Talmudic method is to take the biblical text and apply it to real life.

Think about it like this.

The First Amendment (Amendment I) to the United States Constitution prohibits the making of any law respecting an establishment of religion, ensuring that there is no prohibition on the free exercise of religion, abridging the freedom of speech, infringing on the freedom of the press, interfering with the right to peaceably assemble, or prohibiting the petitioning for a governmental redress of grievances.

Am I allowed to scream fire in a crowded theater? Would that be consistent with the First Amendment right to free speech?

The idea of falsely shouting "fire" in a crowded theater arose from the Supreme Court’s 1919 decision in the case Schenck v. the United States. The Court ruled unanimously that the First Amendment, though it protects freedom of expression, does not protect dangerous speech. In the decision, Oliver Wendell Holmes wrote that no free speech safeguard would cover someone "falsely shouting fire in a theater and causing a panic."

Similarly, the Talmud looks at biblical law and applies it to real world application.