Birkhoff, G. (1940). Lattice theory. American Mathematical Society, Providence, RI. (The third edition appeared in 1967)

Crapo, H. H. and Rota, G. C. (1970). On the foundations of combinatorial theory: Combinatorial geometries. M.I.T. Press, Cambridge, MA.

Tutte, W. T. (1971). Introduction to the theory of matroids. Elsevier, New York.

C. P. Bruter ed. (1971). Théorie des matroïdes. Springer-Verlag, Berlin-New York.

      • W. T. Tutte, Wheels and whirls (1-4)
      • R. A. Brualdi, Generalized transversal theory (5-30)
      • G. W. Dinolt, An extremal problem for non-separable matroids (31-49)
      • J. C. Fournier, Représentation sur un corps des matroïdes d’ordre <= 8 (50-61)
      • A. W. Ingleton, Conditions for representability and transversality of matroids (62-66)
      • M. Las Vergnas, Sur la dualité en théorie des matroïdes (67-85);
      • J. H. Mason, A characterization of transversal independence spaces (86-94)
      • P. Vamos, A.N.S.C. for a matroid to be representable in a vector space over a field
      • D. J. A. Welsh, Matroids and block designs (95-106)

von Randow, R. (1975). Introduction to the theory of matroids. Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin.

Welsh, D. J. A. (1976). Matroid theory. Academic Press, London.

Lawler, Eugene L. (1976). Combinatorial optimization: networks and matroids. Holt, Rinehart and Winston, New York-Montreal, Que.-London.

Schrijver, A. (1978). Matroids and linking systems. Mathematical Centre Tracts, 88. Mathematisch Centrum, Amsterdam.

Brylawski, T. and Kelly, D. (1980). Matroids and combinatorial geometries.Carolina Lecture Series. University of North Carolina, Department of Mathematics, Chapel Hill, N.C.

Barlotti, A., ed. (1982). Matroid theory and its applications. Liguori editore, Naples.

      • Marilena Barnabei, Andrea Brini and Gian-Carlo Rota. An introduction to the theory of Möbius functions (7-109)
      • Andrea Brini. Some remarks on the critical problem (111-124)
      • Thomas Brylawski. The Tutte polynomial. I. General theory (125-275)
      • James G. Oxley. On 3-connected matroids and graphs (277-288)
      • Rhodes Peele. The poset of subpartitions and Cayley’s formula for the complexity of a complete graph (289-297);
      • András Recski. Engineering applications of matroids-a survey (299-321)
      • D. J. A. Welsh. Matroids and combinatorial optimization (323-416)
      • Thomas Zaslavsky. Voltage-graphic matroids (417-424)

Lovász, L. and Recski, A., eds. (1985). Matroid theory. Colloquia Mathematica Societatis János Bolyai 40, North-Holland, Amsterdam.

      • Dragan M. Acketa, Some results on “small” matroids (15-23)
      • Anders Björner, On matroids, groups and exchange languages (25-60)
      • Tom Brylawski, Coordinatizing the Dilworth truncation (61-95)
      • Raul Cordovil, On simplicial matroids and Sperner’s lemma (97-105)
      • Henry Crapo, The combinatorial theory of structures (107-213)
      • François Jaeger, Graphic description of binary spaces (215-231)
      • László Kászonyi, On homogenous forms related to four-colourings (233-238)
      • Bernhard Korte and László Lovász, Posets, matroids, and greedoids (239-265)
      • Jaroslav Nesetril, Svatopluk Poljak and Daniel Turzík, Special amalgams and Ramsey matroids (267-298)
      • Rhodes Peele, Finite partition sublattice representations for some geometric lattices (299-310)
      • András Recski, Some open problems of matroid theory, suggested by its applications (311-325)
      • Alexander Schrijver, Supermodular colourings (327-343)
      • P. D. Seymour, Applications of the regular matroid decomposition (345-357)
      • Éva Tardos, Generalized matroids and supermodular colourings (359-382)
      • Jiörí Touma, Dilworth truncations and modular cuts (383-400)
      • U. Zimmermann, Augmenting circuit methods for submodular flow problems (401-439)

Kung, J. P. S. (1986). A source book in matroid theory. Birkhauser, Boston. This book has the following reprints with commentary

      • Whitney, H. (1932). Non-separable and planar graphs. Trans. Amer. Math. Soc. 34, 339-362.
      • Whitney, H. (1935). On the abstract properties of linear dependence.Amer. J. Math. 57, 509-533.
      • Birkhoff, G. (1935). Abstract linear dependence in lattices. Amer. J. Math.57, 800-804.
      • MacLane, S. (1936). Some interpretations of abstract linear dependence in terms of projective geometry. Amer. J. Math. 58, 236-24.
      • MacLane, S. (1938). A lattice formulation for transcendence degrees and p-bases. Duke Math. J. 4, 455-468.
      • Tutte, W. T. (1947). A ring in graph theory. Proceedings of the Cambridge Philosophical Society 43, 26-40.
      • Tutte, W. T. (1958). A homotopy theorem for matroids, I, II. Trans. Amer. Math. Soc. 88, 144-174. Rota, G. -C. (1964). On the foundations of combinatorial theory. I. Theory of Möbius functions. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 2 1964 340-368.
      • Folkman, J. (1966). The homology groups of a lattice. Journal of Mathematics and Mechanics 15, 631-636.
      • Higgs, D. A. (1968). Strong maps of geometries. J. Combin. Theory 5, 185-191.
      • Dilworth, R. P. and Greene, C. (1971). A counterexample to the generalization of Sperner’s theorem. J. Combin. Theory Ser A. 10, 18-21.
      • Stanley, R. P. (1971). Modular elements of geometric lattices. Algebra Universalis 1, 214-217.
      • Dowling, T. A. and Wilson, R. M. (1975). Whitney number inequalities for geometric lattices. Proc. Amer. Math. Soc. 47, 504-512.
      • Zaslavsky, T. (1975). Facing up to arrangements: Face-count formulas for partition of space by hyperplanes Memoirs of the AMerican Mathematical Society, Providence, R. I.
      • Greene, C. (1976). Weight enumeration and the geometry of linear codes. Studies in Applied Mathematics 55, 119-128.
      • Seymour, P. D. (1979). Matroid representation over GF(3). J. Combin. Theory Ser. B 26, 159-173.
      • Seymour, P. D. (1980). Decomposition of regular matroids. J. Combin. Theory Ser. B 28, 305-359.
      • Kahn, J. and Kung, J. P. S. (1982). Varieties of combinatorial geometriesTransactions of the American Mathematical SOciety 127, 485-499.

White, N., ed. (1986). Theory of matroids. Cambridge University Press, Cambridge.

      • Henry Crapo, Examples and basic concepts (1-28)
      • Giorgio Nicoletti and Neil White, Axiom systems (29-44)
      • Ulrich Faigle, Lattices (45-61)
      • Jospeh P. S. King, Basis-exchange properties (62-75)
      • Henry Crapo, Orthogonality (76-96)
      • James Oxley, Graphs and series-parallel networks (97-126)
      • Thomas Brylawski, Constructions (127-222)
      • Joseph P. S. Kung, Strong maps (224-253)
      • Joseph P. S. Kung and Hien Q. Nguyen, Weak maps (254-271)
      • Hien Q. Nguyen, Semimodular functions (272-297)
      • Thomas Brylawski, Appendix of matroid cryptomorphisms (298-313)

White, N., ed. (1987). Combinatorial geometries. Cambridge University Press, Cambridge.

      • Neil White, Coordinatizations (1-27)
      • J. C. Fournier, Binary matroids (28-39)
      • Neil White, Unimodular matrices (40-52)
      • Richard A. Brualdi, Introduction to matching theory (53-70)
      • Richard A. Brualdi, Transversal matroids (72-96)
      • Raul Cordovil and Brent Lindström, Simplicial matroids (98-113)
      • Thomas Zaslavsky, The Mobius function and the characteristic polynomial (114-138)
      • Martin Aigner, Whitney numbers (139-158)
      • Ulrich Faigle, Matroids in combinatorial optimization (161-211)

Murota, K. (1987). Systems analysis by graphs and matroids. Structural solvability and controllability. Springer-Verlag, Berlin.

Recski, A. (1989). Matroid theory and its applications in electrical network theory and in statics. Springer-Verlag, Berlin.

Korte, B., Lovász, L and Schrader, R. (1991). Greedoids. Springer-Verlag, Berlin.

White, N., ed. (1991). Matroid applications. Cambridge University Press, Cambridge.

  • Walter Whiteley, Matroids and rigid structures (1-51)
  • M. Deza, Perfect matroid designs (54-71)
  • James Oxley, Infinite matroids (73-89)
  • J. M. S. Simoes-Pereira, Matroidal families of graphs (91-104)
  • Ivan Rival and Miriam Stanford, Algebraic aspects of partition lattices (106-120)
  • Thomas Brylawski, The Tutte polynomial and its applications (123-215)
  • Anders Björner, Homology and shellability of matroids and geometric lattices (226-281)
  • Anders Björner and Günter Ziegler, Introduction to greedoids (284-358)

Lawler, E. (1992). Combinatorial optimization: networks and matroids. Holt, Rinehart and Winston, New York.

Oxley, J. G. (1992). Matroid theory. Oxford University Press, New York. (updated 2nd edition 2012).

Truemper, K. (1992). Matroid decomposition. Academic Press, Boston.

Batten L. M. and Beutelspacher A. (1993). The theory of finite linear spaces. Combinatorics of points and lines. Cambridge University Press, Cambridge. (The word matroid is not mentioned in this book but a linear space is a rank-3 matroid.)

Graver, E. J., Servatius, B., Servatius, H. (1993). Combinatorial Rigidity. American Mathematical Society, Providence, RI. Robertson, N. and Seymour, P. D., eds. (1993). Graph Structure Theory, Proceedings of the 1991 AMS-IMS-SIAM Joint Summer Research Conference on Graph Minors. American Mathematical Society, Providence, RI.

Björner, A., Las Vergnas, M., Sturmfels, B., White, N., and Ziegler, G. (1993).Oriented matroids. Cambridge University Press, Cambridge.

Bonin, J., Oxley, J. G., Servatius, B., eds. (1996). Matroid Theory, Proceedings of the 1995 AMS-IMS-SIAM Joint Summer Research Conference. Contemporary Mathematics, 197. American Mathematical Society, Providence, RI.

  • Joseph P. S. Kung, Critical problems (1-127)
  • James Oxley, Structure theory and connectivity for matroids (129-170)
  • Walter Whiteley, Some matroids from discrete applied geometry (171-311)
  • Seth Chaiken, Oriented matroid pairs, theory and an electric application (313-331)
  • Jack Dharmatilake, A min-max theorem using matroid separations (333-342)
  • Gary Gordon and Elizabeth McMahon, A greedoid characteristic polynomial (343-351)
  • Robert Jamison, Monotactic matroids (353-361)
  • S. R. Kingan, On binary matroids with a K3,3-minor (363-369)
  • Laura Chávez Lomelí and Dominic Welsh, Randomised approximation of the number of bases (371-376)
  • Charles Semple and Geoff Whittle, On representable matroids having neither U2,5– nor U3,5-minors (377-386)
  • Tiong-Seng Tay, Skeletal rigidity of p.l.-spheres (387-399)
  • Neil White, The Coxeter matroids of Gelfand et al. (401-409)
  • Open problems (411-418)

Murota, K. (2000). Matrices and matroids for systems analysis. Algorithms and Combinatorics, 20. Springer-Verlag, Berlin.

Borovik, A., Gelfand, I. M. and White, N. (2003). Coxeter Matroids. Birkhauser, Boston 2003.

 Gordon G. and McNulty J.  (2012). Matroids: A Geometric Introduction, Cambridge University Press.

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I am asked sometimes what a matroid is. I often revert to our sacred writings and recall the encounter of Alice with the grinning Cheshire cat. At one stage the cat vanishes away, beginning with the tip of its tail and ending with the grin, which persists long after the remainder of the cat. – W. T. Tutte

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