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The first type of licences are Permissive free software licences, also known as BSD-style licences, or “Copycenter licences”. These licences allow you to do almost anything conceivable with the program and its source code, including distributing then, selling them, using the resultant software for any purpose, incorporating into other software, or even converting copies to different licences, including that of non-free (so-called “proprietary”) software.
Probably the only two actions none of these licences allow is removing the original copyright notice, or suing the creator of the software for damages (the latter is due to the “no warranty” clause). Some of them pose some additional requirements that do not detract from their permissive nature.
Prominent examples of permissive licences include:
The various BSD licences, under which the “Berkeley Software Development” UNIX variant was made available. The original 4-clause BSD licence contained an additional advertising clause, that required publishing the names of the copyright holders on every advertising material. This proved to be a problem and was rendered GPL-incompatible and so using this licence is no longer recommended.
Later on, the advertising clause was removed to formulate the 3-clause and 2-clause BSD licences, which are both less problematic and GPL-compatible.
The MIT X11 License was created by MIT for their X Window System software. It explicitly allows to do many activities with the licensed code, including sub-licensing, which means converting derivative works of the code to different licences.
The Apache License was formulated for the Apache project and has seen several revisions. It includes some language to deal with patent-related issues. The latest version - Apache 2.0 - was partly created in order to be compatible with version 2 of the GPL, but the Free Software Foundation (FSF) claimed that the Apache Licence is incompatible with it. The Apache License, however, was declared as compatible with version 3 of the GPL.
The ISC licence is functionally equivalent to the 2-clause BSD-licence, with some “language made unnecessary by the Berne convention removed”. This licence is also favoured by the OpenBSD project.
Version 2.0 of the Artistic License, which was formulated by The Perl Foundation, is used by the Parrot Virtual Machine, by some Perl 6/Raku implementations, and by other projects. The original Artistic License has problematic phrasing, and is not recommended for general use, unless possibly when dually licensed with a different licence (as is the case for perl 5 and many Perl modules on the CPAN).
An anecdote about this licence is that it was chosen by R.E.M for licensing some video-clips from one of their albums.