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For Biblical Aramaic, there are several good grammars:
For Palestinian Jewish Aramaic, there is one grammar that I am aware of:
For the Aramaic of the Babylonian Talmud and other Jewsih literature, there are several grammars, although I would not recommend them to those unfamiliar with other dialects of Aramaic:
For the Aramaic of the Zohar, there is one grammar that I am aware of, but it is out of print, and in Hebrew:
For Syriac, there is a good pedagogical grammar:
Dictionaries: Both BDB and HALOT mentioned above in the Biblical Hebrew dictionaries section also cover Biblical Aramaic. For later Jewish dialects, a reliable and inexpensive dictionary is Jastrow.
Jeff Berry 2008-04-29