where to start reading theory of logics? I am a student who is working Lie Theory. I want to start read theory of logics. I just need some reference and I have few questions regarding this,
i) will studying theory of logics will improve my theorem proving ability in 'other branch' of mathematics?
ii) is there any results in mathematics, (I am sure there are) (say in algebra particularly in group theory) proof of which is made easy through the approaches and techniques in theory of logics?
iii) where to start reading logic theory and which are good text books in logic theory for the beginners.
I have read Paul R.Halmos  's Naive Set Theory book completely. But I haven't done all the exercises. This is the amount of knowledge I have regarding theory of logics.
I hope I am not confusing between theory of sets and theory of logics.
Thanks for your valuable suggestions.
 A: Yes, there are for example results in algebra that are proved by model-theoretic means (and model theory is usually taken to be a core part of mathematical logic). A classic early example is touched on here http://bit.ly/JKyuuZ And for lots of references to different areas where model theory has got applied more recently, see this MO post and the answers: http://bit.ly/4IXUHa 
The logical resources needed for such applications are pretty sophisticated, but if you want to make a start learning some logic I'm inclined to think that (if you are a good mathematics student) Peter Hinman's Fundamentals of Mathematical Logic is perhaps the go-to book if you want a single textbook to get you into the field. It is very lucid. True, it is a Very Big Book, but that's because it covers a lot at an accessible pace -- and the preface explains very well how to steer a course through the book to suit particular interests.
For an extensive annotated reading Guide to logic more generally, looking at lot of textbooks at different levels, you can download the PDF http://bit.ly/18t5CUD (which doesn't yet given an account of Hinman's book -- a major shortcoming that will be corrected in the next version). The Guide has a section on model theory in particular.
