I would recommend a few different texts. Chiefly, since you are looking for something basic and fundamental, I would encourage you to check out Yitzhak Frank, Grammar for Gemara and Targum Onkelos (Jerusalem, 2009). He goes into detail as regards the relationship of different Aramaic dialects to one another, their relationship with Hebrew (Biblical and Mishnaic) and presents a basic grammar of Talmudic language. For what you are looking for, this might be the best bet.
If you wanted something a little bit less "basic", but somewhat more direct as regards the relationship between Aramaic and Hebrew, have a look at Sabatino Moscati (et al), An Introduction to the Comparative Grammar of the Semitic Languages (ed. S. Moscati; Wiesbaden, 1980), or Patrick R. Bennett, Comparative Semitic Linguistics: A Manual (Eisenbrauns, 1998), which is somewhat more basic than its title suggests.
So too, if you decide that you want something that focuses a little more heavily on the grammar of the language and less on its relationship to Hebrew, I personally found very useful Alger F. Johns, A Short Grammar of Biblical Aramaic (Michigan, 1972) and Wm. B. Stevenson, Grammar of Palestinian Jewish Aramaic (Oxford, 1962) - although note that neither of these are for the gemara. The first will help with Daniel, Ezra and some targumim and the second with the Yerushalmi (and various other targumim), but unless you are going to delve into a lot of detail, I don't think you'll find either so different from the grammar of the Bavli that they will fail to be of assistance there either.
Finally, and if only because nobody else ever mentions it in this context, you can never go wrong with a good grammar of Syriac. Although it will necessitate learning a different script (and depending on how readily you learn scripts, that may or may not be much of a setback), but the grammar is virtually indistinguishable from Babylonian Talmudic Aramaic. For my money, the best three grammars of Syriac are:
Takamitsu Muraoka, Classical Syriac: A Basic Grammar with a Chrestomathy (Wiesbaden, 1997);
Theodore H. Robinson, Paradigms and Exercises in Syriac Grammar (4th ed; Oxford, 1962);
W.M. Thackston, Introduction to Syriac (Maryland, 1999).