Here are a few suggestions (which depending on your background may be more or less useful):

1. Logic and Structure 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 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 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 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 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 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 by Stephen C. Kleene. A classic text in mathematical logic which is still a rewarding read.
8. Open Logic Project - is a collection of teaching materials on mathematical logic aimed at a non-mathematical audience, intended for use in advanced logic courses as taught in many philosophy departments. It is open-source: you can download the LaTeX code. It is open: you’re free to change it whichever way you like, and share your changes. It is collaborative: a team of people is working on it.

I hope these (admittedly biased) suggestions are some use!

Here are a few suggestions (which depending on your background may be more or less useful):

1. Logic and Structure 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 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 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 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 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 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 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!

Here are a few suggestions (which depending on your background may be more or less useful):

1. Logic and Structure 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 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 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 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 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 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 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!

Here are a few suggestions (which depending on your background may be more or less useful):

1. Logic and Structure 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 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 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 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 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 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 by Stephen C. Kleene. A classic text in mathematical logic which is still a rewarding read.
8. Open Logic Project - is a collection of teaching materials on mathematical logic aimed at a non-mathematical audience, intended for use in advanced logic courses as taught in many philosophy departments. It is open-source: you can download the LaTeX code. It is open: you’re free to change it whichever way you like, and share your changes. It is collaborative: a team of people is working on it.

I hope these (admittedly biased) suggestions are some use!