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Subversion and the Apache Subversion logo are registered trademarks of The Apache Software Foundation. Several companies (Collab Net, WANdisco, Visual SVN, elego, ...) pay or have payed the salaries of some full-time developers, but the software carries an Apache License which is fully compliant with the Debian Free Software Guidelines.
In other words, you are free to download, modify, and redistribute Subversion as you please; no permission from any company or any person is required. It is mature software, with strong compatibility guarantees.
Writing programs to access the repository is similar to writing programs that use other filesystem APIs.
The main difference is that this particular filesystem doesn't lose data when written to; old tree states can be retrieved as easily the most recent state.
If you want to host a networked repository, then you need to set up either Apache2 or an "svnserve" server. If you want Web DAV and all the other "goodies" that come with the Apache server, then yes, you'll need Apache 2.0.
For more details about setting up a network accessible Subversion server, see chapter 6 in the Subversion book. It's always an option to run Apache 2.0 on a different port while continuing to run Apache 1.x on port 80.
(This is similar to how branches and tags are conventions built on top of copies, instead of being basic concepts built into Subversion itself.) Each time you commit a change, the repository stores a new revision of that overall repository tree, and labels the new tree with a new revision number.
Of course, most of the tree is the same as the revision before, except for the parts you changed.
See chapter 6 in the Subversion book to learn more. The long answer: if you just want to access a repository, then you only need to build a Subversion client.
FSFS repositories (introduced in version 1.1) do not have this restriction; however, due to a limitation in Win9x's file-locking support, they also don't work in Win9x.
To reiterate, the Subversion client can be run on any platform where APR runs.
The Subversion client will run anywhere APR runs, which is most places.
The Subversion server (i.e., the repository side) is the same, except that it will not host a Berkeley DB repository on Win9x platforms (Win95/Win98/Win ME), because Berkeley DB has shared-memory segment problems on Win9x.