Legality of universities posting sections of books online Something I have noticed in my courses over the years is that in addition to all the online distributions of textbooks (which I understand to be mostly illegal), I can often times find universities posting sections of books online, particularly just the exercises. Doesn't this violate the same copyright law?

Here are some examples of what I am referring to from books I have studied from in the past.

Do Carmo, Differential Geometry of Curves and Surfaces

Here is a solution manual to about half of Brown and Churchill's book in complex analysis (sections of the book itself can be found as well, and it may be worth noting that this is not the university the authors were associated with, I don't know).

There are other examples from other pretty well known texts in mathematics.

How is this legal for universities to do? Do they need to consult the publisher or something first?
First of all, copyright infringement on this scale, which is not done for financial gain (in most common law countries) is not illegal but unlawful. The difference between these two things is that illegal behavior can lead to punishment, whereas unlawful behavior is simply not protected by law - if you are doing something lawful, you are protected from someone seeking redress. If someone seeks redress from you because you have distributed their copyright work, you cannot argue that your behavior was permitted by law.

With this in mind, it's not necessarily an important question whether or not your university is doing something which infringes copyright. In theory, everything is either lawful or unlawful, legal or illegal, with nothing in between. In practise, the only person who might reasonably be able to determine this is a judge (assisted by several lawyers). Partly because the time of judges and lawyers is costly, whole areas of human behavior exist in gray areas which are not in anyone's best interest to resolve one way or the other.

People break the law all the time. Some laws are never enforced, and some laws are unenforceable. Everyone is familiar with urban myths about various commonplace things such as Christmas pudding, or kissing on a Sunday being illegal in various jurisdictions, other practices such as outdoor nudity or urination being technically legal although they might be expected to lead to arrest, and yet further things such as weekly archery practice being required by law. Some of these stories are completely true, by the letter of the law. Large organizations such as Apple and Microsoft agree on wide-ranging 'patent swaps' rather than try to figure out who is infringing whom. Doubtless any organization as large as a university is constantly breaking some law or other, if you include building codes, employment regulations, health and environmental restrictions, tax codes, immigration requirements, etc. Probably lots of people are employed to do nothing except check that the university meets the regulations, but these people are constantly playing catch-up to new rules, as well as trying to make sure that the thousands of people working within the institution are obeying the internal policies which call for compliance to the law, rather than disregarding them (as they usually are).

Now, most academic publications are both written by academics and mainly bought by them, as well as by academic libraries. Academics are paid by universities to do research which includes the writing of books, and while lots of textbook publishers are corporations, some belong to universities, or work in joint ventures with universities. Thus publishers, authors, editors and readers of these books together with university organizations form a community. For publishers to spend their time trying to investigate instances of copyright infringement like the one you mentioned, would be the equivalent of you constantly remeasuring the borders of your backyard, trying to determine the exact boundary line ever more precisely, asking your neighbours to tear down fences and re-erect them a few inches over, and snipping the branches of plants which overlapped by a small amount. While your legal right, it would be very detrimental to the community, in this case the community of people who live in your neighbourhod, of which you are part. It would also be a huge waste of your time, for little or no benefit.

Far more important than legality is the question of ethical behavior. Unlike the law, one is not expected to attempt to conform as best one can, but to behave completely ethically, and make it clear that one is behaving ethically, at all times. The flip side of this is that you cannot behave unethically by accident, or without your own knowledge.

For a textbook publisher to reprint (say) a complete collection of one academic's papers which were published on her website, without notifying her or asking her approval, would be completely unethical, even if they were stated to be in the public domain. Similarly, it would be unethical for that academic to turn her university homepage into a site called 'FreeTextbookz' with a large collection of files and paid banner advertising. Many things which fall in between this are accepted by consensus of the community as being benign or trivial.