Good book for studying $S_\infty$.

I'm looking for any books with some good information involving $S_\infty$ and other Polish groups. Specifically interested in $S_\infty$. This is an extremely amazing topological group, now having witnessed metrizability and admittance of a left invariant metric by Birkhoff-Kakutani. I have recently come across some interesting questions involving how to ascertain a complete metric given a left invariant metric, and whether or not a bi-invariant metric exists. I'm confident, that I have the answer to both, but would prefer a little more "reading material," before I post my answers on here to be destroyed by the math geniuses of the world.

Books and notes I already have or have access to:

Kechris, Descriptive Set Theory; Moschavakis, Set Theory; Dikran Dikranjan, Intro. to topological groups.; Willard, General Topology; Munkres, Topology.

Thanks in advance for all input.

Solution 1:

There are:

• M. Bhattacharjee, D. Macpherson, R. Möller, and P. M. Neumann, Notes on infinite permutation groups, 1997.
• P. J. Cameron, Permutation groups, Cambridge University Press, 1999.
• J. Dixon, and B. Mortimer, Permutation groups, Springer-Verlag, 1996.

The first reference is specifically about infinite permutations groups, the other two have some content about infinite permutation groups.