This volume grew out of a desire by the editors to honor their teacher, Roger Lyndon, on the occasion of his sixty-fifth birthday. Five short articles about Lyndon and his contributions to mathematics, as well as twenty-seven invited research papers in combinatorial group theory and closely related areas are contained in this book. It is a tribute to Lyndon's mathematical breadth that papers covering such a wide array of topics are all closely related to the work he has done. Several of the articles fall into subfields of combinatorial group theory, areas in which much of the initial work was done by Lyndon. Remaining research articles fall into various subfields of homological groups, another area in which he has made major contributions. Research articles, written by some of the leading practitioners in the field, are listed below.There is a biographical essay about Lyndon by Kenneth Appel, and there are expository articles about his work by Saunders MacLane, John Ratcliffe, Jerome Keisler and Paul Schupp. MacLane describes the results in Lyndon's doctoral thesis and explains how they fit into the early history of spectral sequences while Ratcliffe presents Lyndon's fundamental work in cohomology of groups in the early part of his career. His work in logic, especially his fundamental results in model theory in the mid 1950s is discussed by Keisler. Lyndon's contribution to group theory over the past twenty years is described by Schupp.
List of Research Articles: IA-automorphisms of free products of abelian groups by S. Andreadakis On Artin groups and Coxeter groups of large type by K. I. Appel The finite generation of $Aut(G)$, $G$-free metabelian of rank $\geq 4$ by S. Bachmuth and H. Y. Mochizuki Two-generator groups III by J. L. Brenner, R. M. Guralnick, and J. Wiegold The subgroup separability of free products of two free groups with cyclic amalgamation by A. M. Brunner, R. G. Burns, and D. Solitar Another proof of the Grushko-Neumann-Wagner theorem for free products by R. G. Burns and T. C. Chau On varietal analogs of Higman's embedding theorem by F. B. Cannonito On the Whitehead method in free products by D. J. Collins and H. Zieschang Quadratic parametric equations over free groups by L. P. Comerford, Jr. and C. C. Edmunds Finite groups of outer automorphisms of a free group by M. Culler A remark on automorphism groups by J. L. Dyer On three of Lyndon's results about maps by L. Greendlinger and M. Greendlinger On the indecomposability of certain relation cores by K. W. Gruenberg Fox subgroups of free groups II by N. Gupta Extension of groups by tree automorphisms by N. Gupta and S. Sidki Length functions and algorithms in free groups by A. H. M. Hoare Split extensions of abelian groups with identical subgroup structures by C. Holmes Non-planarity of planar groups with reflections by J. Huebschmann A survey of the conjugacy problem by R. D. Hurwitz Maximal algebras of binary relations by B. Jonsson Uber untergruppen ebener diskontinuierlicher gruppen by R. N. Kalia and G. Rosenberger Automorphisms of a free product with an amalgamated subgroup by A. Karrass, A. Pietrowski, and D. Solitar Some remarks on braid groups by A. Karrass, A. Pietrowski, and D. Solitar Geometric realization of group extensions by the Seifert construction by K. B. Lee and F. Raymond The augmentation quotients of the groups of order $2^4$ by G. Losey and N. Losey Finite-dimensional algebras and $k$-groups of finite rank by A. G. Myasnikov and V. N. Remeslennikov The cohomology ring of a one-relator group by J. G. Ratcliffe Combinatorial group theory, Riemann surfaces and differential equations by C. L. Tretkoff and M. D. Tretkoff.