A very incomplete list of papers and books on groupoids (or that mention groupoids) arranged chronologically (by publication date)

1981

Brown, Ronald, and Higgins, P.J., The algebra of cubes,  J. Pure Appl. Alg. 21 (1981), 233-260.

    This paper shows that w-groupoids and crossed complexes are equivalent.

Brown, Ronald, and Higgins, P.J., Colimit theorems for relative homotopy groups, J. Pure Appl. Alg. 22 (1981), 11-41.

    The authors work with equivalences of w-groupoids and crossed complexes.

Brown, Ronald, and Higgins, Philip J., The equivalence of w-groupoids and cubical T-complexes, Cah. Top. Geom. Diff. (3 Coll. sur les categories dedie a Charles Ehresmann) 22 (1981), 370-386.

O.M. Gornostaev, Extensions of Orders with Partial Subgroupoids of Semigroups, Contemporary Algebra. Semigroup Constructions Leningrad State Pedagogical Institue, Leningrad (1981), 4-9.

    In Russian.

1982

Higgins, P.J. and Taylor, J., The fundamental groupoid and homotopy crossed complex of an orbit space in Category theory: Proceedings Gummersbach 1981, K.H. Kamps et. al. (eds), (Springer Lecture Notes in Mathematics 962) Springer-Verlag, Heidelberg (1982) 115-122.

Ramsay, Arlan, Topologies on measured groupoids, J. Funct. Anal. 47 (1982) 314-343.

Renault, Jean, C*-algebras of groupoids and foliations, Proc. Sympos. Pure Math. 38 Part I, Amer. Math. Soc., Providence, R.I., (1982) 339-350.

Taylor, J. Group actions on w-groupoids and crossed complexes, and the homotopy groups of orbit spaces, Ph.D. thesis, University of Durham (1982).

1983

Brown, Ronald, Heath, P.R., and Kamps, K.H., Groupoids and the Mayer-Vietoris sequence, J. Pure Appl. Alg. 30 (1983), 109-129.

Reinhart, Bruce L., Differential geometry of foliations, Springer-Verlag, 1983.

    Mainly a study of foliations, this book includes two sections related to groupoids - one is an introduction to groupoids in the context of differential geometric structures and the other is on the classifying space for a topological groupoid.

Winkelnkemper, H., The graph of a foliation, Ann. Global Analysis and Geometry 1:3 (1983), 51-75.

    The graph of a foliation is also known as the holonomy groupoid.

1984

Brown, Ronald, Some non-abelian methods in homotopy theory and homological algebra in Categorical topology: Proc. Conf. Toledo, Ohio, 1983 H.L. Bentley et al, (eds), Heldermann, Berlin (1984) 108-146.

    This paper gives an overall view of the role and significance of some categories, including w-groupoids and \infty-groupoids and their relationships.

Brown, R., Heath, P.R., and Kamps, H.K., Coverings of groupoids and Mayer-Vietoris type sequences, Categorical topology: Proc. Conf. Toledo, Ohio, 1983 H.L. Bentley et al, (eds), Heldermann, Berlin (1984) 147-162.

    This paper generalizes the results of the paper by the same authors in 1983 in the Journal of Pure and Applied Algebra and gives some new applications.

Dwyer, W.G. and Kan, D.M., Homotopy theory and simplicial groupoids, Proc. Kon. Nederl. Akad. Wet. A 87  (1984) 379-385.

Haefliger, A., Groupoides d'holonomie et classifiants, Asterisque 116 (1984) 70-97.

Kumjian, Alexander, On Localizations and Simple C*-Algebras, Pacific Journal of Mathematics, 112 (1984) 141-192

    Kumjian shows that each free localization is associated to a unique principal r-discrete groupoid with Haar system.

Park, J.S. and Lee, K.H., Groupoid as a covering space, Bull. Korean Math. Soc. 21 (1984) 67-75.

1985

Masuda, Tetsuya, Groupoid dynamical systems and crossed product in Operator Algebras and their Connections with Topology and Ergodic Theory, Proceedings of the OATE Conference held in Busteni, Romania, Aug. 29-Sept. 9, 1983, Lecture Notes in Mathematics, 1132 (350-361), Springer-Verlag, New York, 1985.

Razak, Salleh, A. and Taylor J., On the relation between the fundamental groupoids of the classifying space and the nerve of an open cover, J. Pure Appl. Alg. 37 (1985) 81-93.

Renault, Jean, Representations des produits croses d'algebres des groupoids, Publ.Math. Univ. Pierre et Marie Curie 70, 1985.

Renault, Jean, Two applications of the dual groupoid of a C*-algebra in Operator Algebras and their Connections with Topology and Ergodic Theory, Proceedings of the OATE Conference held in Busteni, Romania, Aug. 29-Sept. 9, 1983, Lecture Notes in Mathematics, 1132 (434-445), Springer-Verlag, New York, 1985.

    The two applications are that Kumjian's diagonal algebras give "good" transversals for the dual groupoid and that the dual groupoid naturally defines a generalized Dixmier-Douady invariant for an arbitrary C*-algebra.

1986

Pradines, J., Quotients de groupoides differentiables, C.R. Acad. Sci. Paris Ser. I Math. 303 (1986), 817-820.

Seda, A.K., On the continuity of Haar measure on topological groupoids, Proc. Amer. Math. Soc. 96 (1986) 115-120.

Takesaki, M., A classification theory based on groupoids, Proc. of the US-Japan Seminar, Kyoto, 1983, Pittman Research Notes in Math. Ser., 123 (1986), 400-410.

Ver Ecke, P., Sur la classifiant du groupoide fundamental d'un feuilletage, Proc. Kon. Nederl. Akad. Wet A 89 (1986) 179-200.

1987

Aof, Mohamed El-saeed Abbdel-Fattah, Topological aspects of holonomy groupoids, Ph.D. Thesis, University of Wales, 1987.

Brown, Ronald, From groups to groupoids: a brief survey, Bulletin of the London Mathematical Society, 19, (1987), 113-134.

    This paper contains a fairly lengthy accounting of the usage of groupoids until the mid 1980's.  There is particular emphasis on the use of groupoids in topology, which is Brown's interest.

Brown, Ronald and Higgins, P.J., Tensor products and homotopies for w-groupoids and crossed complexes, J. Pure Appl. Algebra, 47 (1987), 1-33.

Ehresmann, C., Oeuvres completes et commentees (A. C. Ehresmann, ed.) Suppl. Cahiers Top. Geom. Diff., Amiens, 1980-1984.

Mackenzie, K., Lie groupoids and Lie algebroids in differential geometry, Cambridge University Press, 1987.

    In the introduction, Mackenzie states that "The concept of groupoid is one of the means by which the twentieth century reclaims the original domain of application of the group concept."  With an emphasis on connection theory, this book is both a summary of known results on differentiable and Lie groupoids and their Lie algebroids, along with some previously unpublished results by the author on the "abstract theory of transitive Lie algebroids, their cohomology theory, and the integrability problem and its relationship to connection theory."

Mackenzie, K.C.H., A note on Lie algebroids which arise from groupoid actions, Cahiers Topologie Geom. Differentielle Categoriques 28 (1987), 283-302.

Muhly, Paul, Renault, Jean, and Williams, Dana, Equivalence and isomorphism for groupoid C*-algebras, Journal of Operator Theory 17 (1987), 3-22.

Phillips, J., The holonomic imperative and the homotopy groupoid of a foliated manifold, Rocky Mountain J. Math. 17 (1987), 151-165.

    Phillips compares the holonomy groupoid and the F-fundamental groupoid and shows that they are both Lie groupoids.

Ramsay, Arlan, Topologies for measured groupoids, Journal of Functional Analysis, 47 (1987), 314-343.

Renault, Jean, Representation des produits croises d'algebres de groupoides, J. Operator Theory 18 (1987) 67-97.

Tilson, Bret, Categories as Algebra: An Essential Ingredient in the Theory of Monoids, Journal of Pure and Applied Algebra, 48 (1987), 83-198.

    Mainly a treatise on monoids, the paper contains two results concerning connected groupoids and local monoids.

Weinstein, Alan, Symplectic groupoids and Poisson manifolds, Bull. Amer. Math. Soc. (N.S.), 16 (1987) 101-104.

    This is a research announcement on how one uses the notion of symplectic groupoids to answer questions about "universal enveloping algebras" for quasiclassical approximations to nonlinear commutation relations.  The details are found in the following publication:

Coste, A., Dazord, P., Weinstein, A., Groupoides symplectiques, Publications du Departement de Mathematiques, Universite Claude Bernard-Lyon I 2A (1987), 1-67.

1988

Bourn, Dominique, Pseudofunctors and non-abelian weak equivalences in Categorical Algebra and its Applications, Proceedings of a Conference held in Louvain-La-Neuve, Belgium, July 26-August 1, 1987, Lecture Noes in Mathematics, 1348 (1988), 55-71.

    The author uses the notion on n-groupoid to develop a non-abelian equivalent to the notion of chain complex in the development of a cohomology theory.

Brown, Ronald, Topology: a geometric account of general topology, homotopy types and the fundamental groupoid, Second Edition, Ellis Horwood Limited, West Sussex, England, 1988.

    This book is the second edition of the book which originally appeared in 1968.  In the preface of this edition, Brown claims that his topology book is the only English text on topology in print that uses the notion of the fundamental groupoid to explore notions in homotopy.  He expands his treatment of morphisms and on the fundamental groupoid in this edition.

Mikami, K., and Weinstein, A., Moments and reduction for symplectic groupoids, Publ. Res. Inst. Math. Sci. 24 (1988), 121-140.

Moerdijk, I., The classifying topos of a continuous groupoid, Trans. Amer. Math. Soc., 310 (1988), 629-668.

Moerdijk, I., Toposes and groupoids in Categorical Algebra and its Applications, Lecture Notes in Mathematics, 1348, Springer, Berlin, 1988, 280-298.

Moore, Calvin C. and Schochet, Claude, Global Analysis on Foliated Spaces, Springer-Verlag, New York, 1988.

    This book examines the topological groupoid of a foliation in the case of a foliated bundle with discrete structural group and the case of the Reeb foliation.  It contains a chapter on measurable and topological groupoids and the notion of transverse measures on foliated spaces.  It also discusses the operator algebras associated with groupoids and in particular the groupoid of a foliated space.

Pradines, J., Remarque sur le groupoide cotangent de Weinstein-Dazord, C.R. Acad. Sci. Paris Ser. I Math. 306 (1988), 557-560.

Renault, Jean and Moran, B., Ideal structure of groupoid crossed product C*-algebras, Miniconferences on harmonic analysis and operator algebras (Canberra, 1987), 267-268, Proc. Centre Math. Anal. Austral. Nat. Univ. 16 Austral. Nat. Univ. Canberra, 1988.

Taylor, J. Quotients of groupoids by the action of a group, Math. Proc. Camb. Phil. Soc. 103 (1988) 239-249.

Weinstein, A., Coisotropic calculus and Poisson groupoids, J. Math. Soc. Japan, 40  (1988), 705-727.

1989

Brown, Ronald, Symmetry, groupoids, and higher-dimensional analogues.  Symmetry 2:  unifying human understanding, Part 1, Comput. Math. Appl. 17 (1989), 49-57.

Cuesta, F. Alcalde, Groupoide d'homotopie d'un feuilletage riemannien et realisation symplectique de certaines varietes de Poisson,  Publicacions Matematiques, 33 (1989), 395-410.

Golodets, Valentin Ya. and Sinelshchikov, Sergey D., Regularization of actions of groups and groupoids on measured equivalence relations, Pacific Journal of Mathematics, 137 (1989) 145-154.

    The authors define actions on measured groupoids and formulate the notion of semidirect product of a measured groupoid by a locally compact group of nonstrict automorphisms.

Lasso de la Vega, M., Groupoide fondamental et d'holonomie de certains feuilletages reguliers, Publicacions Matematiques 33 (1989), 431-443.

Lu, J-H., and Weinstein, A., Groupoides symplectiques doubles des groupes de Lie-Poisson, C.R. Acad. Sci. Paris Ser. I Math. 309  (1989), 951-954.

Mackenzie, K.C.H., Classification of principal bundles and Lie groupoids with prescribed gauge group bundle, J. Pure Appl. Algebra 58 (1989), 181-208.

    This paper uses Lie groupoids to develop the classification of principal bundles.

Nambooripad, K.S.S., and Pastijn, F.J., Amalgamation of regular semigroups, Houston Journal of Mathematics 15 (1989), 249-254.

    This paper applies ordered groupoids to inverse semigroups.

Schultz-Heinecke, B., Zur Vollstandigkeit der induktiven Gruppoide der partiellen Automophismen von Algebren, Periodica Mathematica Hungarica 20 (1989), 115-145.

1990

Dazord, P., Groupoides symplectiques et troisieme theoreme de Lie "non lineaire," Lecture Notes in Mathematics 1416 39-74, Springer-Verlag, New York, 1990.

Daletskii, A. Yu, The factorization problem in a symplectic groupoid and Hamiltonian systems on spaces with nonlinear Poisson brackets, Soviet Mathematics - Doklady, 40 (1990), 389-

Ge, Zhong, Generating functions, Hamilton-Jacobi equations and symplectic groupoids on Poisson manifolds, Indiana University Mathematics Journal, 39 (1990) 859-

Higgins, P.J. and Mackenzie, K.C.H., Fibrations and quotients of differentiable groupoids, J. London Math. Soc. 42 (1990), 101-110.

Lawson, M.V., The geometric theory of inverse semigroups I:  the reduced case, Journal of Pure and Applied Algebra, 67 (1990) 151-177.

    This paper applies ordered groupoids to inverse semigroups.

Moerdijk, I., The classifying topos of a continuous groupoid II, Cahiers de topologie et geometrie differentielle categoriques, 31 (1990), 137-

Muhly, Paul S. and Williams, Dana P., Continuous trace groupoid C*-algebras, Mathematics scandinavica, 66 (1990), 231-

Muhly, Paul S., and Solel, Baruch, On triangular subalgebras of groupoid C*-algebras, Israel Journal of Mathematics, 71 (1990), 257-

O'uchi, M., A C*-algebra for a reduction of a holonomy groupoid, Mathematica Japonica, 35 (1990), 493-

Ramsay, Arlan, The Mackey-Glimm dichotomy for foliations and other Polish groupoids, J. Functional Analysis, 94 (1990), 358-374.

J. Usan, Partial A_t Groupoids, Zb. Radova Prir. Mat. Fac. Univ. Novyi Sad 17 (1990), 109-127.

    In Russian.

Xu, P., Morita Equivalence of Symplectic Groupoids and Poisson Manifolds, Ph.D. thesis, University of California at Berkeley, 1990.