Alan Turing’s research paper On Computable Numbers, with an Application to the Entscheidungsproblem appeared in the Proceedings of the London Mathematical Society. Alan Turing later published A Correction to that paper in that same journal as well. If you are a subscriber to the Proceedings of the London Mathematical Society, or if you have access to it via your Institution, you can view these research papers for free and see them as they were originally published.

However, if you simply Google the title of the paper, you’ll find that copies of this paper exist in many places all over the internet. (Some of these websites are listed below.) This may not be too surprising, since this research paper is one of the great landmarks in the history of mathematics, so you would expect that it is being read and reread by many people.

There is a book that contains not only Alan Turing’s famous paper in its entirety, along with his latter published correction (and also further corrections by other mathematicians), but also other papers and correspondences written by Turing during his lifetime. It is the book The Essential Turing edited by B. Jack Copeland (Oxford University Press, 2013). For example: It includes Alan Turing’s letter to Winston Churchill, in which he requested additional resources needed to crack the German Enigma; Turing’s famous article “Computing Machinery and Intelligence” that appeared in Mind (1950), pp. 433-60, where he proposed “The Imitation Game” (more commonly known today as “The Turing Test”) as a way of deciding whether a computer has the intelligence of a human; as well as other articles about Chess, Artificial Intelligence, Artificial Life, Solvable and Unsolvable Problems, and others.

As is well known to graduate students in mathematics, published research papers are notoriously terse, leaving the details and computations to be completed by the reader. For that reason, such papers are often read with the help of a pencil and paper, and it often takes days to get through a single page. Furthermore, for papers having long expressions of mathematical symbols, it is not uncommon for typos to somehow creep in on the way to publication. Experts in the field will easily recognize the typos, but others may end up questioning their own sanity. Therefore, if you seriously intend to read and understand Alan Turing’s “On Computable Numbers, with an Application to the Entscheidungsproblem”, then I strongly recommend that you read the book The Annotated Turing by Charles Petzold (Wiley Publishing, Inc., 2008), where the author first prepares you with all the information you need before you can start reading the paper, and then proceeds through the entire paper, giving ample explanations after almost every line or paragraph, and pointing out the typos as he corrects them.

One way to get a copy of Alan Turing’s original paper is to first go to the webpage on Alan Turing in Wikipedia. If you scroll down to almost the bottom of that page, you’ll see a heading Works of Turing and under it the line “Alan Turing’s publications indexed by Google Scholar.” In that line, if you click on the link Alan Turing’s publications, then it’ll take you to a page where you can click on links to Alan Turing’s papers. Then, if you click on the link On computable numbers, with an application to the Entscheidungsproblem, it will take you to a page that has a link to a copy of this paper as a pdf file.

This website in French is devoted to a Turing Machine built by Marc Raynaud. Among its many links is a page with 18 videos and a link to Alan Turing’s original paper.

Here is another webpage with Alan Turing’s original paper. It is part of an interesting website with links to many interesting topics. This website is maintained by abelard, who claims to “live in a ger on the steppes of outer mongolia, surrounded by an indeterminate number of yaks, …”