Is there any halacha prohibiting the study of the Talmud for non-Jews?
A gentile is permitted to learn the seven commandment that are applicable to gentiles, because this is needed for them to know, however other than that he should not learn torah. The reason is because the Torah is considered like the “bride” of the Jewish nation. In fact there is even a prohibition for a Jew to teach a gentile Torah.
Talmud Sanhedrin 59a, see Rashi and Meiri, Midrash Tanchuma Mishpotim 5, Rambam (Melachim) 10-9.