The publisher asks me whether I want a CC-BY, CC-BY-NC, CC-BY-ND or a CC-BY-ND-NC. What do these abbreviations mean?

They refer to various Creative Commons licences.

CC-BY

CC-BY is the Creative Commons Attribution licence.

With a Creative Commons Attribution licence (CC-BY), everyone has permission to distribute, copy and modify your work on the condition that you are credited for the work. Modifying refers to translating, abridging, summarising or otherwise altering the work.

CC-BY-ND

The abbreviation ND stands for 'no derivatives', meaning that derivative work is prohibited.

With a CC-BY-ND licence, you permit the distribution and copying of your work on the condition that you are credited for the work, but you do not permit your work to be modified. In other words, your work may not be translated, edited or otherwise altered without your permission. The advantage of this is that no one can 'mess up' your work. A disadvantage is that if someone wants to translate or abridge your work or save it in a different format, this person first has to ask for your permission (and that of any co-authors) as long as the copyright applies. 

CC-BY-NC

The abbreviation NC stands for 'non-commercial use', meaning that commercial use is prohibited.

With a CC-BY-NC licence, you permit the distribution, copying and modification of your work on the condition that you are credited for the work, but you do not permit your work to be used for commercial purposes. In other words, your work may not be used commercially without your permission (and that of your co-authors).

In some cases, commercial use is clear, as in a company 'selling' your work despite the fact that it is freely available elsewhere. The problem is that there is a grey area when it comes to commercial use. Commercial use is not clearly defined: is it commercial use to index your work and make it easy to find on Google, to use it as part of a private collaboration or to reproduce it at the price of printing? For this reason, the use of NC is not recommended. 

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Latest modifications 06 Jul 2016