I am an active part of a research project on the positive effects of open math projects on the community. With open math projects I have in mind a particular thing, namely a GIT project on mathematics in which everyone can contribute and the final result is a collaborative text about some part of mathematics. The obvious examples are The stacks project, The HoTT book, Open logic project. I would like to know other examples of this kind of project. I am specially interested in those projects that have already finished (succeeded).
5 Answers
Here are six fairly specific examples that I know of; in each case, the writers have welcomed collaboration.
 Eric Peterson's formal geometry notes, on using bordism operations and some formal algebraic geometry in homotopy theory. Though the class is complete, the notes are still in progress.
 Eric Peterson's vector fields on spheres notes, from a class taught by Haynes Miller. These notes are still in progress.
 Sanath Devalapurkar's notes from two algebraic topology classes taught by Haynes Miller.
 Andy Neitzke's notes on applications of quantum field theory to geometry, for a class currently being taught at UT Austin (so the notes are still in progress).
 Andy Neitzke's notes on the moduli space of Higgs bundles, from a class taught a few years ago.
 My notes on equivariant homotopy theory, from a class taught by Andrew Blumberg. The notes are stable, but not completed.
There's some repos I know:
William Stein (wellknown for SageMath) has two books on github: one on the Riemann hypothesis and one on algebraic number theory.
Jim Hefferon's Linear Algebra book has its source on gitlab. It's mostly Jim committing there, though.
nomeata (Joachim Breitner) has set up a wiki for scribe notes from the Karlsruhe university long ago. It's still active, and the sources are now on github.
The MathComp book is not about maths per se but about a proof assistant (the MathComp/ssreflect "dialect" of Coq).
The CRing project was meant to be like the Stacks project, but for commutative algebra. It seems to have lost traction, but there are 493 pages written already! (NB: It has my name on the contributors list because at some point I gave them permission to use one of my TeX files, but they never ended up using it.)
I tried this a few times myself:
Infinitedimensional Lie algebras (notes from a class by Pavel Etingof). These notes cover something like 1/2 of the class (all that I have fully understood). Arguably a lot of things could be improved (the subject is typically done with an amount of handwaving unusual for algebra, and I had to introduce some formalism to make things rigorous; this formalism is often awkward). I really wouldn't mind if someone came along and continued the job ;)
Notes on the combinatorial fundamentals of algebra. The basics of combinatorics (permutations, signs, etc.) necessary to build up determinants, and some determinantal identities, written up in high detail and with numerous exercises. (The length is due to the detailed proofs; the content itself covers perhaps half of a semester of discrete maths and algebraic combinatorics.)
I tried writing notes for a linear algebra class and for a graph theory class. Result is I got the first 45 (resp. 23) lectures written up, then dropped it, as I ran out of time. Probably needs more iterations (or a 1/0 teaching load...).

2$\begingroup$ The current CRing project seems to be now maintained by Markus J. Pflaum, who also has another open book project FANCy on Functional Analysis and Noncommutative Geometry. Both have git repositories. $\endgroup$ Oct 3, 2017 at 7:26
There is also this project for number theory, it seems to be be a very great and vast text:
I have a github page for my lecture notes on exterior differential systems. The final document, to date: Introduction to exterior differential systems.
We use Git+GitHub to manage both the development of the software powering the piBase community database of topological spaces and its underlying dataset.
git
repos with lecture notes qualify? – I maintain such a project, but the number of contributors is negligible … sadly $\endgroup$