How does Judaism in the modern world differ from the Judaism of Tanakh? What traditions do they share?

Answer 1

While based in the Torah, Judaism as it is practiced today is filtered through Rabbinic-era texts, primarily the Talmud and medieval legal codes, such as the Mishneh Torah of Maimonides and the Shulchan Aruch of Rabbi Joseph Caro. Also, it is important to know that there is not one type of Judaism practiced today; there are many. Without going into great detail, the different streams of Judaism differ on the importance of these later texts and how they apply today. So while Jews celebrate Biblical holidays, for example, they way they are celebrated differs greatly from how the Torah commands, in great part because there is no Temple in which to offer sacrifices; prayer has replaced sacrifice - and that makes a great difference.