A theme im noticing in history is that Jews were prosecuted and hated, from the Romans to the middle ages to Nazis. What was the reason for this? I'm asking specifically in middle ages Europe but information about earlier periods is also welcome.
The simple answer is that in Christian Europe, Jews were considered guilty of the crime of deicide, the murder of Christ, a belief the Roman Catholic Church did not renounce until Vatican II in the 1960s. Because of this, Jewish people were outsiders to a society built around Christian ideals and values, and indeed, represented a threatening social other. They were also a convenient scapegoat for any and all social problems, as the many episodes of violence and expulsions from various countries and regions throughout the Middle Ages show. Generally, Jews existed in tension with the ideal, cohesive Christian society that the medieval Church sought to implement through its work to structure governments, institutions of learning, and rituals, and as such, were legitimised as a target for outbursts of violence that were otherwise prohibited. Christians were forbidden to kill one another, as knights often made a hobby of doing in the 9th and 10th centuries, but by the 11th, with the Peace of Christ instituted, they had to turn their murderous hobbies outwards. First, that meant Jewish communities, and then ultimately, on to Crusading.
There are a lot of reasons for anti-Jewish and later, anti-Semitic behaviour throughout the Middle Ages. Theological ideas played a part -- Jews not only killed Christ, they rejected Christianity, and so, according to St Augustine of Hippo, they were a cursed "remnant people" who existed solely to show Christians what happened when you displeased God and bore the brunt of that divine displeasure. Preachers used Jews as a shorthand for demonic, devilish, malicious, greedy, and evil, fabricating stories about Jews desecrating the Eucharistic Host (the Body of Christ when transubstantiated) because they hated Jesus just so much that they had to stab a wafer; they also told stories about Jews murdering Christian children to use the blood in Passover matzah. The accusation of blood libel, particularly offensive when kashrut, the Jewish dietary laws, prohibit the consumption of blood of any kind, has hung on for a long, long time, and crops up in modern anti-Semitic screeds. Jews also were forced into the social role of moneylenders, as Christians were theologically forbidden to lend money. Thus, Jewish moneylenders gathered a great deal of liquid capital, which made them a target of ire, especially during economic downturns. The trope of borrowing gold from Jewish lenders then exiling the Jews from your kingdom so you don't have to pay it back was so widespread that it pops up in medieval video games like "Crusader Kings." It happened frequently, and it's why Jews were associated with usury -- charging interest.
Basically, this is a huge topic that historians have been arguing about for a long time, especially in the wake of the Holocaust, and is constantly changing as we better understand religious and cultural sensibilities in the ancient and medieval world. If this is your first foray into antisemitism, I really recommend starting with Steven Beller's Antisemitism: A Very Short Introduction, part of the Oxford University Press's Very Short Introduction series. It'll give you a good overview, and then prepare you for some deeper dives, like these:
Carroll, James. Constantine's Sword: The Church and the Jews. A History. Boston, New York: Mifflin, 2002.
Nirenberg, David. Anti-Judaism: The Western Tradition. New York: W.W. Norton & Company, 2013.
Nirenberg, David. Communities of Violence: Persecution of Minorities in the Middle Ages. Princeton: Princeton University Press, 2015.
Langmuir, Gavin L. History, Religion, and Antisemitism. Berkely: University of California Press, 1993.
Lipton, Sara. Dark Mirror: The Medieval Origins of Anti-Jewish Iconography. New York: Metropolitan Books, 2014.
Rubin, Miri. Gentile Tales: The Narrative Assault on Late Medieval Jews. Philadelphia: University of Pennsylvania Press, 2004.