I am reading a classic book in mathematics that was published in the 1960s. This book uses very old notation, which makes it impossible to read it. Suppose further that I want to read the whole book and, in the process, retype it using modern notation, without any addition. Can I do it freely?
Please do notice I do not aim to publish it. Would I be allowed to share it without any copyright violation? Obviously, writing the name of the original author as “the real author”.
For your own use, you can type anything you like, modify it in any way that you like. There are no restrictions on that sort of thing, as long as it is strictly for personal use. Among other reasons, a copyright holder would have no knowledge on which to base a case and no particular incentive to make a legal case.
The problems would occur depending on what you mean by "share it". Within in a small research group there would likely be no copyright violations (likely "fair use"). Putting in on a website without the copyright holder's permission is almost certainly a violation.
The question of when "sharing" becomes "re-publication" can be a bit subtle, but the balance is probably more with the copyright holder. Translations and derivative works are protected under most copyright laws. One of the considerations in most copyright law is what is the effect on the value of the original. Things that reduce the value, which your ideas would seem to do, are normally violations.
It might be worth talking to the original publisher. They might be interested in what you want to do, and hold the rights to enable it. You could wind up with your name on the cover, along with the original author(s).
In US law, this would be considered a derivative work. If the book is still under copyright (which is pretty much certain for any book published in 1964 or later), then you would need permission from the copyright holder to distribute the work in any way.
There are certain exceptions in US law ("fair use") that would allow you to distribute the revised book without the permission of the copyright holder. But these probably do not apply here, particularly since you are planning to distribute the entirety of the book (rather than a small section) and it would potentially impact the sales of the existing book (since people would use your version rather than the older one.)
Conversely, if the book has entered the public domain (which is possible if the book was published in 1963 or earlier), then you can create and distribute derivative works without any restrictions.
This would definitely be copyright infringement, as discussed in the other answers. BUT: if the book is a good work that’s still relevant today, you could be doing the world a huge favor by retyping it. The economics of textbook publishing are such that only a very small number of classic books from the pre-TeX era have been retypeset to modern standards of readability/searchability/accessibility. The Feynman Lectures on Physics volumes, which were converted into both LaTeX and HTML, are one example. But for books that don’t have the large reach of such a classic and popular work, there is no hope for this type of digital facelift without a passionate champion like you who is interested in putting in the time and work to make it happen.
What I’d suggest is that you contact the publisher and ask if they’d be interested in publishing a new edition of the book if you were to retypeset it yourself free of charge. They might say yes and authorize you to go ahead. This will be a win-win for you, them, and any readers interested in the book. If the publisher or copyright holder is not interested in profit (or if the book is in such a niche topic that they won’t expect to make any profit), they might conceivably even approve for you to share the new version online free of charge. (It doesn’t seem very likely, but it never hurts to ask…) So: good luck!
This depends on your school's fair use policy as well as how you share it and the publisher's policy. In short, it's complicated and it depends on lots of stuff. Here are some rules from where I live, that will hopefully give you information to go looking for where you live:
Fair use: Some schools have "fair use" policies that explicitly allow you to copy parts of a text for teaching purposes. However, most of the time this does not cover the entire text. The specifics of how much is too much varies from school to school, so you'll need to understand it for your institution.
How it is shared: sharing for non-commercial purposes among a small group of people is sometimes, but not always, allowed, and will depend on your country and the country in which the book was copyrighted. Generally, if the copyright doesn't even apply in your country it's not illegal, but some countries have rules that state you can make copies for non-commercial use, often within some rules (like limits on the type of copies and how widely they are distributed)
The publisher's policy: Copyright extends 50 years beyond the death of the author in my country, but it may be different for you. This copyright can be extended by the publisher, or the book could be released into the public domain before any of this happens. You can always look into it. The publisher may also be out of business...
I think that if you are going to go to the trouble of re-writing the entire book you can probably just write your own at that point, but if you intend to just share it among your class and it is your own project you are unlikely to run into any issues.
