Syriac can be considered an eastern dialect of Aramaic. There's a debate about whether it should be counted as a dialect or as its own separate language, but in any case it's Aramaic. There are some grammatical differences from biblical Aramaic (which is western Aramaic); for instance, third masculine imperfect verb forms begin with nun instead of yod, and the plural emphatic of masculine nouns ends in ē instead of ayyā. Of course, there's also some distinctive vocabulary. Because Syriac became the language of the Christian church in the Middle East, there is a vast body of theological, liturgical, mystical, martyrological, etc., literature that uses specialized Christian terminology, some of it borrowed from Greek, some of it translated from Greek, some of it developed within Syriac.
Originally Posted by ISalzman
If you know biblical Aramaic, you'd need to adjust to these differences (as well as to different scripts), but it probably wouldn't be that hard. If you know some Jewish Talmudic Aramaic (Jewish Babylonian Aramaic), which is also an eastern form of Aramaic, even some of the grammar might be familiar.
As a matter of fact, yes.
By the way, you're not the same David R who authored the Epistles of John in the Westminster Bible Companion Series, are you?