Books:

1. Orbifolds and Stringy Topology (Cambridge Tracts in Mathematics) (Hardcover) by _Alejandro Adem_ (Author), _Johann Leida_ (Author), _Yongbin Ruan_ (Author) *Key Phrases: *_orbifold groupoid_ , _inertia orbifold_ , _orbifold vector bundle_ , _Chen-Ruan Dolbeault _ (It is not on MathNetSci yet for some reasons).

2. Weinberger.Shmuel
The topological classification of stratified spaces. Chicago Lectures in Mathematics. /University of Chicago Press, Chicago, IL,/ 1994. xiv+283 pp.
3. tom Dieck, Tammo

Transformation groups. de Gruyter Studies in Mathematics, 8. /Walter de Gruyter & Co., Berlin,/ 1987. x+312 pp.

Surveys:

1. Adem.Alejandro ; Davis, James F. Topics in transformation groups. /Handbook of geometric topology, /1--54, /North-Holland, Amsterdam,/
2002.
2. D'Ambra, G. ; Gromov, M. Lectures on transformation groups: geometry and dynamics. /Surveys in differential geometry (Cambridge, MA, 1990), /19--111, /Lehigh Univ., Bethlehem, PA,/ 1991.
3. Davis, Michael W.
Nonpositive curvature and reflection groups. /Handbook of geometric topology, /373--422, /North-Holland, Amsterdam,/ 2002.
4. Yu, Guoliang
Higher index theory of elliptic operators and geometry of groups. /International Congress of Mathematicians. Vol. II, /1623--1639, /Eur. Math. Soc., Zich,/ 2006.