I come to this discussion with the assumption that Christians and Jews are brothers in arms against the Muslims desire for global Jihad. But my son sent me some verses from the Talmud that make it sound like Jews could also conduct Jihad against Christians if they so desire to interpret the Talmud in such light. Thank you for your consideration to my question.

Shalom, To answer in short: No there is no concept of Jihad in the Talmud . For more details, I first want to say, I appreciate your request for clarification out of sincerity , for this supposed quote as I shall clarify, has been used antagonistically numerous times over the generations to slander or attack Jews. Secondly, your caption for your question, Abodah Zara 26, is incorrect, and I add, that the quote" the best of the Gentiles should be killed" is found nowhere in the Talmud itself. This point itself is quite significant because the Talmud is the source of codification for Jewish law unlike other texts from the Talmudic scholars= "midrash" of the same period in time, which are texts of homiletic nature and do not serve as a source for Jewish law. So, before, I even get into what is the accurate quote in its source in these homiletic texts, it should be clear that this quote is not codified anywhere in the code of Jewish law, therefore there is no such thing as a Jewish Jihad, and what you were told is inaccurate. The source of the quote is in a homiletic text called the Mekhilta on the book Exodus 14:7 which offers an exegesis of explaining where the Egyptians got their horses from in order to chase after the Israelites who had left Egypt since scripture states that they died during the plague as it says in Exodus 9:6. The Mekhilta then offers the explanation that the horses were from the Egyptians who feared the word of G-d and during the plague of hail they had chased their cattle to go indoors so they don't get hurt. In that context, Rabbi Simeon Bar Yohai says " The best of Egyptians should be killed and the best of snakes, crush its skull. " The version in most parallel Rabbinic texts is Egyptians , NOT gentiles. What does this Rabbi Simeon come to tell us? The act of the Egyptians chasing their cattle indoors may have seemed innocent at the time. There was no wrong doing of them wanting to save their possessions. However, when the Israelites left Egypt, the price of this "innocent" act wasn't innocent at all. The horses which were saved were now pursuing the Israelites to bring them back to slavery or worse. This will also explain the juxtaposition of mentioning crushing the skull of a snake. For a person at one point may have felt, that he should not harm a dangerous snake. But then when later the same snake lunges at the person with a venomous bite, the person wishes that he had crushed the skull of that snake earlier to remove the danger. Now, I will not conceal from you, that there are versions of this phrase which say " Even the best of the Gentiles should be killed' and not Egyptians as I said before. But these same later versions of this phrase appear in a text called "Masechet Sofrim" " also add " Even the best of the Gentiles should be killed IN THE TIME OF WAR". To explain this, I will bring an explanation which was offered more than a hundred years ago during the Beilis trial in 1913 by Rabbi Samuel Isaac Hilman. The Beilis trial , took place in Russia when a Jew was falsely accused for murdering a Christian child and was later acquitted. Rabbi Hilman was appointed chief Rabbi of Glasgow, Scotland in 1908 and then in 1914 went to be the Chief of the Rabbinical court in London. His explanation appeared in the newspapers of London and Glasgow and was very much accepted by the readers. He said, there is no way for Rabbi Simeon to have something to allow the murder of a gentile, when the prohibition to murder is written explicitly in the Ten commandments and doesn't distinguish between Jew of non-Jew. On the other hand, the phrase "Even the best of the Gentiles should be killed in the time of war" neither needs to be said to permit the killing of an enemy. Because when an army wages war in self- defense or to protect others the standard laws of killing do not apply and in warfare taking the lives of others is not the same as in peacetime. While war is terrible thing, this is pretty much the standard around the world. So, if that is the case what was Rabbi Simeon's intention? Rabbi Hilman explained that sometimes it may occur during war that a soldier may meet in battle on the opposite side of enemy lines the same person who is known to him as a good and decent person. But now this person is now on the opposite side of enemy lines, do I then not harm him? For this reason, Rabbi Simeon came to teach us that in the heat of battle the person who may have know otherwise is now there to kill you and in this case he up stands up to kill you, you should be first to kill him. Similarly wrote the 16th century Rabbi Judah Loew , know as the Maharal of Prague , who also lived in a period of blood libels against the Jewish people. "The meaning is not to kill a gentile. Our Sages never said that one should kill gentiles; Heaven forbid to say so. Rather, the meaning is the following: in war. When a gentile comes against you in battle and falls into your hand in that same war—do not have mercy on him at all. This was the situation in Egypt, where the Egyptians came against Israel and killed them and their children. It is about such cases that the Sages said ‘kill.’ Similarly, in the book Deutronomy 20:3): ‘Hear, O Israel, you are drawing near today to battle against your enemies’—meaning that if they fall into your hands, do not show them mercy, because they will not show mercy to you This applies to gentiles who come against Israel in war and are Israel’s enemies, fighting them. Rabbi Loew continues to say: But regarding gentiles who have done good to Israel, we are commanded by the Holy One, blessed be He, not to do them harm. Even the Egyptians themselves, who killed Israel’s children and made them suffer harsh slavery—because Israel dwelled in their land, God commanded us to show kindness to their descendants, as it says (Deut. 23:8): ‘Do not despise an Egyptian, for you were a stranger in his land.’ How much more so with gentiles who do not harm Israel, that we should not repay them with harm. How could the words of the Sages contradict this verse, which explicitly commands doing good to those who do good to us? While there is still so much to say, I will suffice with this. I think I made it clear what the meaning on the phrase is, and clearly there is no mention in the Talmud to kill gentiles. All the best