Here are a few suggestions (which depending on your background may be more or less useful): 1. [Logic and Structure][1] by Dirk van Dalen. I have used this as a textbook when teaching mathematical logic and for that purpose it is decent. Some people find it a bit dry, but at least it covers a large amount of material in a reasonably clear manner. 2. [Mathematical Logic][2] by Joseph R. Shoenfield. This book is, I think, regarded by many logicians as being the gold standard text on the subject. 3. [A Course in Mathematical Logic][3] by John Bell and Moshe Machover. This is my personal favorite textbook in mathematical logic. (Unfortunately, it's a North Holland book and so is a bit less affordable.) 4. [A Course in Mathematical Logic for Mathematicians][4] by Yuri I. Manin (with contributions from Boris Zilber). I think that pretty much anything written by Manin is worth taking seriously and this book is no exception. 5. [Notes on Logic and Set Theory][5] by Peter T. Johnstone. This is a delightful little (literally) book on logic which is highly recommended (perhaps in conjunction with one of the other larger books from this list). 6. [The Mathematics of Metamathematics][6] by Helena Rasiowa and Roman Sikorski. This is a nice book which gives a lattice theoretic development of mathematical logic. (Difficult to find, but worth a look if your library has a copy.) 7. [Introduction to Metamathematics][7] by Stephen C. Kleene. A classic text in mathematical logic which is still a rewarding read. I hope these (admittedly biased) suggestions are some use! [1]: http://www.amazon.com/Logic-Structure-Dirk-van-Dalen/dp/3540208798/ref=sr_1_1?ie=UTF8&s=books&qid=1279898385&sr=8-1 [2]: http://www.amazon.com/gp/product/1568811357/ref=s9_simh_gw_p14_i2?pf_rd_m=ATVPDKIKX0DER&pf_rd_s=center-2&pf_rd_r=004B9VBMP4N0PF8KBS7K&pf_rd_t=101&pf_rd_p=470938631&pf_rd_i=507846 [3]: http://www.amazon.com/Course-Mathematical-Logic-John-Bell/dp/0720428440/ref=sr_1_1?ie=UTF8&s=books&qid=1279898811&sr=1-1 [4]: http://www.amazon.com/Course-Mathematical-Mathematicians-Graduate-Mathematics/dp/1441906142/ref=sr_1_1?ie=UTF8&s=books&qid=1279898941&sr=1-1 [5]: http://www.amazon.com/Notes-Theory-Cambridge-Mathematical-Textbooks/dp/0521336929/ref=sr_1_3?ie=UTF8&s=books&qid=1279899249&sr=1-3 [6]: http://www.amazon.com/Mathematics-Metamathematics-Helena-Sikorski-Rasiowa/dp/B002FKDA1Y/ref=sr_1_2?ie=UTF8&s=books&qid=1279899446&sr=1-2 [7]: http://www.amazon.com/Introduction-Metamathematics-Stephen-Cole-Kleene/dp/0923891579/ref=sr_1_1?ie=UTF8&s=books&qid=1279899322&sr=1-1