Rules for using an electronic text as the texbook for a class I have just completed my PhD in Mathematics and accepted a job as a visiting assistant professor. The course I am assigned to teach allows me to pick the textbook I wish to use. 

I am currently looking for lower-cost/free textbook options for my students, and I have found a textbook that I really like in the SpringerLink database. My school’s library has a subscription to this database which give students access to an electronic copy of this book free of charge. Are there any rules which prevent me from assigning this as the textbook for the class and giving them the option to download it for free through the library?
Well .. one idea is to assign the book as the textbook then notify the students that they should get the book via buying from amazon ... or that your library has access to Springer resources free of charge for the students. University students are adults that can make their own decisions.

As the course coordinator you are not selling the book, and it is not your responsibility to hand in a book to each student. Students can: buy the book or use free resources on their own progeratives. Students are not liable, since they are just accessing your library to view already available resources.

As long as you do not directly post content such as homework questions or chapter text from the book or directly share such content in any way, such as on the course website or as handouts, you are not liable. You are just assigning a book as recommended textbook and notifying the students their options. Students are also not liable since your library enables them to access free material they wish to view.

I also just want to give an example of clear violation. If you buy the book and make a pdf out of it and share them in course site (does not matter whether public access or not) that would be a breach of copyright.