Beginner material for mathematical logic I am looking for study and beginner material to study mathematical logic. I understand that it is a very broad topic but I would like to know what the best path there is to learning mathematical logic. Where should one start? What are the best resources? If someone could paint a time line of events that should take place in order to gain a good understanding of mathematical logic, that would be fantastic. I have seen this question but it does not give the depth I require. 
 A: *

*For a heavily annotated and detailed Guide to teaching yourself logic by a selection from the many many available books, try my Teach Yourself Logic at http://www.logicmatters.net/students/tyl/  It aims precisely to enable a student to move on "step-by-step".

*I'm not sure quite what you mean by "paint[ing] a time line of events that should take place in order to gain a good understanding of mathematical logic"; but TYL does have a crude map of the way areas of mathematical logic relate to each other which might help.
A: I want to give an alternative approach to Peter Smith selection of books, what IMO is more aimed to philosophers than mathematicians. 
IMHO the best introductory book of mathematical logic that you can read is the first two (or maybe three) chapters of A concise introduction to mathematical logic of Wolfgang Rautenberg.
Also it is very hard to beat, in rigor, the first two chapters of Introduction of mathematical logic of Elliot Mendelson or the first chapters of Mathematical logic of Tourlakis.
The big problem that I found in almost all introductory books to mathematical logic is that when the authors try to make things easier (as an introductory text demand) they do just wrong, appealing to informal reasons to show how to be formal!
