There are currently four Big Red Logic Books, with a fifth due sometime in 2023 (to be realistic).
The first two were previously published by CUP. But I have recovered the copyright, and as a small gesture to students in these very hard times they are now published as open-access PDFs, entirely free to download. They are also available as minimum cost paperbacks using the Amazon print-on-demand system (because this produces acceptable-quality books very inexpensively).
Before I retired from the University of Cambridge, it was my greatest good fortune to have secure, decently paid, university posts for forty years in leisurely times, with almost total freedom to follow my interests wherever they meandered. Like most of my contemporaries, for much of that time I didn’t really appreciate how extraordinarily lucky I was. To give a little back by way of heartfelt thanks, I’ve also put together two further student-oriented books, which are again free to download. In particular, Beginning Mathematical Logic is developed from the much-used Teach Yourself Logic study guide.
An Introduction to Formal Logic was originally published by Cambridge University Press (2003, 2020). It began life as lecture notes for a course for first-year philosophers which I taught for many years.
A corrected version of the second edition is now available as a freely downloadable PDF. Many people, however, prefer if possible to work from a physical book. So you can get a print-on-demand copy of IFL as a very inexpensive large-format paperback from Amazon. There is also a nice but still inexpensive hardback version intended for libraries.
For more info, see here, where you will also find answers to exercises etc.
An Introduction to Gödel’s Theorems was first published in 2007 also by Cambridge University Press, with the second edition appearing in 2013. It was published in a philosophy series, but is full of theorems — so many mathematics students should find it useful too.
A corrected version of the second edition is now available as a freely downloadable PDF. Again, for people who prefer to work from a physical book, there is a print-on-demand version as a very inexpensive large format book from Amazon.
For more info, see here where you will also find further support documents.
Gödel Without (Too Many) Tears is a much shorter book (2020) based on my notes for the lectures I used to give to undergraduate philosophers taking the Mathematical Logic paper in Cambridge. These have now been tidied-up into a book format. You can think of it as a cut-down version of the longer Gödel book, aiming to give some of the key technical facts about the incompleteness theorems without too many digressions.
This book is again available as a PDF. There is also an extremely inexpensive print-on-demand book available from Amazon, and a hardback too.
NEW! If you want to self-study logic, or are looking for supplementary reading before or during a university course, how do you find your way around the very large literature old and new? Beginning Mathematical Logic (2022) provides a study guide, giving introductory overviews of the core topics and then recommending the best books for studying these topics enjoyably and effectively.
This book too is available as a PDF. There is also a very inexpensive print-on-demand book available from Amazon
A few years back wrote some notes on category theory (running to almost 300 pages). And despite their very rackety half-baked form, they are downloaded startlingly often — almost a thousand times in January 2022.
I’m really pretty embarrassed to leave the notes online in their current state. On the other hand, having putting the work in earlier, I’m reluctant to trash them. Which leaves the remaining option, of getting down to more work and and making a better fist of it. Starting in February 2022, this will take quite a lot of time, but (I hope) not too many tears. Meanwhile,