Book that is more accessible than Shoenfield My logic course is based on my Computer Science education and on some random Internet pages (mostly Wiki). I want to make my knowledge of logic more coherent and fill in missing gaps. Thus I started reading  Shoenfield's "Mathematical Logic" but I don't like this book. I found it to terse (almost no examples) and quite vague. I would like to read something more accessible yet rigorous enough about first order logic and something really brief and basics about model theory. I study by myself so I need some exercises, best with answers (no need for full solution) so I can be reassured that I understand topic well.
 A: I'm not sure whether it is "wonderful" as Hunan Rostomyan very kindly says, but for what it is worth here's [a link to] an extensive Guide to the textbooks out there:

http://www.logicmatters.net/tyl

And yes, Shoenfield's Mathematical Logic is almost certainly not the place to start (it is indeed "terse", though "vague" is the wrong word -- "tough" would be better!). So certainly, don't be put off learning more logic by the fact that you found that particular book hard going. If you have a bit of maths/compsci background, you could find the widely available book by Enderton works well -- but there are other suggestions in the Guide. Just browse through a few options till you find one at the level that suits you best.
A: When I teach a course on this at the undergrad level, I use Enderton's book A Mathematical Introduction to Logic. It is very well written, and it conveys the right viewpoint, in a certain sense. 
An online resource is a set of lecture notes by Stephen Simpson, which you can find on his webpage. The "Mathematical logic" and "Foundations of Mathematics" notes cover about two semesters of introductory logic. 
For model theory, a reasonable and modern book, which is not too advanced at the beginning chapters, is Marker's Model Theory: An Introduction. 
A: May I recommend Elliot Mendelson's 'Mathematical logic', CRC Press?  Earlier editions were not nicely printed but later ones are ok.  One problem with later editions is that they have been padded with material not really at the heart of the subject - but you can skip them!  Solutions to many (but not all) of the exercises are included.  The rudiments of model theory are included.
