Sources

There is much more here than we will possibly present in a semester in any detail. I suggest focussing on the references in bold type, and even those we will only sample the content of: concentrate on background and on key results and examples.

Baumslag's papers on the ArXiv
MathSciNet's listing of Baumslag's papers

1. Background
   • Baumslag, Topics in Combinatorial Group Theory, ETH, Zurich 1987/88, Chapter 1
   • Rotman, Introduction to the Theory of Groups
   • Miller, Decision problems for groups – survey and reflections
   • Baumslag, Boone, Neumann, Some unsolvable problems about elements and subgroups of groups, Math. Scand. 7, 191-201


2. non-Hopfian groups and residual finiteness
   • Baumslag and Solitar, Some two-generator one-relator non-Hopfian groups, Bull. Amer. Math. Soc. 68 1962 199–201
   • Notes of Robert I. Campbell on Residual Finiteness
   • Baumslag, Automorphism groups of residually finite groups. J. London Math. Soc. 38 1963 117-118
   • Magnus, Residually finite groups, Bull. Amer. Math. Soc. Volume 75, Number 2 (1969), 305-316
   • Baumslag, Finitely generated cyclic extensions of free groups are residually finite. Bull. Austral. Math. Soc. 5 (1971), 87–94


3. Free groups and Marshall Hall's Theorem
   • Baumslag, Myasnikov, Remeslennikov, Malnormality is decidable in free groups, Internat. J. Algebra Comput. 9 (1999), no. 6, 687-692
   • Baumslag, Bogopolski, Fine, Gaglione, Rosenberger, Spellman, On some finiteness properties in infinite groups, Algebra Colloq. 15 (2008), no. 1, 1-22


4. Peculiar finitely presented groups
   • Baumslag, A non-cyclic one-relator group all of whose finite quotients are cyclic, J. Austral. Math. Soc. 10 1969 497-498
   • Baumslag and Miller, Some odd finitely presented groups, Bulletin of the London Math. Soc. 20 (1988), 239-244
   • Baumslag, Miller, Troeger, Reflections on the residual finiteness of one-relator groups, Groups Geom. Dyn. 1 (2007), no. 3, 209-219


5. One-relator groups (2 weeks?)
   • Baumslag, A survey of groups with a single defining relation, Proceedings of groups–St. Andrews 1985, 30–58, London Math. Soc. Lecture Note Ser., 121, Cambridge Univ. Press, Cambridge, 1986
   • Baumslag, Reflections on the residual finiteness of one-relator groups. (English. English summary), Groups Geom. Dyn. 1 (2007), no. 3, 209–219
   • Baumslag, Groups with one defining relator (Survey), J. Austral. Math. Soc. 4 1964 385–392
   • Baumslag, Some open problems, Summer School in Group Theory in Banff, 1996, 1-9, CRM Proc. Lecture Notes, 17, Amer. Math. Soc., Providence, RI, 1999
   • Baumslag, Myasnikov and Shpilrain, Open Problems in combinatorial and geometric group theory
   • Baumslag, Miller, A remark on the subgroups of finitely generated groups with one defining relation. Illinois J. Math. 30 (1986), no. 2, 255–257.
   • Wise's solution to Baumslag's question about residual finiteness of torsion-free 1-relator groups: section 18 of these notes


6. The topology of discrete groups
   • Baumslag, Dyer, Heller, The topology of discrete groups. J. Pure Appl. Algebra 16 (1980), no. 1, 1–47
   • Baumslag, Dyer, Miller, On the integral homology of finitely presented groups. Bull. Amer. Math. Soc. (N.S.) 4 (1981), no. 3, 321–324


7. Wreath-products
   • Baumslag, Wreath products and finitely presented groups. Math. Z. 75 (1961), 22–28
   • Baumslag, Bridson, Gruenberg, On the absence of cohomological finiteness in wreath products, J. Austral. Math. Soc. Ser. A 64 (1998), no. 2, 222–230
   • Baumslag, Embedding wreath-like products in finitely presented groups. I., Geometric methods in group theory, 197-206, Contemp. Math., 372, Amer. Math. Soc., Providence, RI, 2005


8. Metabelian groups
   • Baumslag, A finitely presented metabelian group with a free abelian derived group of infinite rank. Proc. Amer. Math. Soc. 35 (1972), 61–62
   • Baumslag, Some reflections on finitely generated metabelian groups (survey), Combinatorial group theory (College Park, MD, 1988), 1-9, Contemp. Math., 109, Amer. Math. Soc., Providence, RI, 1990
   • Baumslag, A finitely presented solvable group that is not residually finite. Math. Z. 133 (1973), 125–127
   • Baumslag, On finitely presented metabelian groups. Bull. Amer. Math. Soc. 78 (1972), 279
   • Baumslag, Stammbach, Strebel, The free metabelian group of rank two contains continuously many nonisomorphic subgroups. Proc. Amer. Math. Soc. 104 (1988), no. 3, 702
   • Baumslag, Cannonito, Robinson, The algorithmic theory of finitely generated metabelian groups, Trans. Amer. Math. Soc. 344 (1994), no. 2, 629-648
   • Baumslag, Mikhailov, Orr, A new look at finitely generated metabelian groups, Computational and combinatorial group theory and cryptography, 21–37, Contemp. Math., 582, Amer. Math. Soc., Providence, RI, 2012


9. Parafree groups
   • Baumslag, Parafree groups (survey), Infinite groups: geometric, combinatorial and dynamical aspects, 1-14, Progr. Math., 248, Birkhauser, Basel, 2005
   • Baumslag, Cleary, Havas, Experimenting with infinite groups, Experiment. Math. 13 (2004), no. 4, 495-502
   • Baumslag, Cleary, Parafree one-relator groups, J. Group Theory 9 (2006), no. 2, 191-201


10. Residually torsion-free nilpotent groups
    • Baumslag, Finitely generated residually torsion-free nilpotent groups. I., J. Austral. Math. Soc. Ser. A 67 (1999), no. 3, 289–317
    • Baumslag, Musings on Magnus, The mathematical legacy of Wilhelm Magnus: groups, geometry and special functions (Brooklyn, NY, 1992), 99–106, Contemp. Math., 169, Amer. Math. Soc., Providence, RI, 1994
    • Baumslag, Miller, The isomorphism problem for residually torsion-free nilpotent groups. (English. English summary), Groups Geom. Dyn. 1 (2007), no. 1, 1-20.
    • Baumslag, Some reflections on proving groups residually torsion-free nilpotent. I, Illinois J. Math. 54 (2010), no. 1, 315–325
    • Baumslag, Mikhailov, Residual properties of groups defined by basic commutators


11. Algorithmic unsolvability in small cancellation and hyperbolic groups
    • Baumslag, Topics in Combinatorial Group Theory, ETH, Zurich 1987/88, Section 7 of Chapter 1
    • Gersten, Introduction to hyperbolic and automatic groups, notes from a CRM Summer School on Groups held at Banff in August 1996
    • Baumslag, Miller, Short, Unsolvable problems about small cancellation and word hyperbolic groups, Bulletin of the London Math. Soc. 26 (1994), 97-101


12. Subdirect products, Fiber products
    • See this blog post for background
    • Baumslag and Roseblade, Subgroups of direct products of free groups. J. London Math. Soc. (2) 30 (1984), no. 1, 44-52
    • Baumslag, Bridson, Miller, and Short, Fibre products, non-positive curvature, and decision problems — groups G that are both CAT(0) and hyperbolic and yet such that G × G has a finitely presented subgroup whose distortion is not bounded above by any recursive function. See also the 1-2-3 Theorem: 5.16 in III.Gamma of Bridson and Haefliger, Metric Spaces of Non-Positive Curvature.
    • Baumslag, Bridson, Holt, Miller, Finite presentation of fibre products of metabelian groups, J. Pure Appl. Algebra 181 (2003), no. 1, 15-22


13. Automaticity, isoperimetric functions
    • Baumslag, Miller, Short, Isoperimetric inequalities and the homology of groups. Invent. Math. 113 (1993), no. 3, 531–560
    • Baumslag, Gersten, Shapiro, Short, Automatic groups and amalgams—a survey, Algorithms and classification in combinatorial group theory (Berkeley, CA, 1989), 179–194, Math. Sci. Res. Inst. Publ., 23, Springer, New York, 1992
    • Baumslag, Gersten, Shapiro, Short, Automatic groups and amalgams. J. Pure Appl. Algebra 76 (1991), no. 3, 229–316
    • Baumslag, Bridson, Miller, Short, Finitely presented subgroups of automatic groups and their isoperimetric functions, J. London Math. Soc. (2) 56 (1997), no. 2, 292-304


14. Group theoretic cryptography
    • Baumslag, Fine, Xu, Cryptosystems using linear groups, Appl. Algebra Engrg. Comm. Comput. 17 (2006), no. 3-4, 205-217
    • Baumslag, Fine, Xu, A proposed public key cryptosystem using the modular group, Combinatorial group theory, discrete groups, and number theory, 35–43, Contemp. Math., 421, Amer. Math. Soc., Providence, RI, 2006
    • Baumslag, Camps, Fine, Rosenberger, Xu, Designing key transport protocols using combinatorial group theory, Algebraic methods in cryptography, 35-43, Contemp. Math., 418, Amer. Math. Soc., Providence, RI, 2006
    • Baumslag, Bryukhov, Fine, Rosenberger, Some cryptoprimitives in noncommutative algebraic cryptography, Aspects of infinite groups, 26-44, Algebra Discrete Math., 1, World Sci. Publ., Hackensack, NJ, 2008
    • Baumslag, Bryukhov, Fine, Troeger, Challenge response password security using combinatorial group theory, Groups Complex. Cryptol. 2 (2010), no. 1, 67-81
    • Baumslag, Fazio, Nicolosi, Shpilrain, Skeith, Generalized learning problems and applications to non-commutative cryptography, Provable security, 324–339, Lecture Notes in Comput. Sci., 6980, Springer, Heidelberg, 2011


15. Algebraic geometry over groups
    • Baumslag, A survey of groups with a single defining relation, Proceedings of groups–St. Andrews 1985, 30–58, London Math. Soc. Lecture Note Ser., 121, Cambridge Univ. Press, Cambridge, 1986
    • Baumslag, Myasnikov, Remeslennikov, Algebraic geometry over groups, Algorithmic problems in groups and semigroups (Lincoln, NE, 1998), 35–50, Trends Math., Birkh ̈auser Boston, Boston, MA, 2000


16. Other
    • Baumslag, A finitely generated, infinitely related group with trivial multiplicator. Bull. Austral. Math. Soc. 5 (1971), 131–136
    • Baumslag, Gruenberg, Some reflections on cohomological dimension and freeness. J. Algebra 6 1967 394-409

1. N.Brady, Riley, Short, The Geometry of the Word Problem for Finitely Generated Groups
2. Bridson and Haefliger, Metric Spaces of Non-Positive Curvature
3. Brown, Cohomology of Groups
4. Bux, Groups and Spaces, Volume I: Groups, Volume II: Spaces
5. Davis, The Geometry and Topology of Coxeter Group
6. Epstein et al., Word Processing in Groups
7. Geoghegan, Topological Methods in Group Theory Theory
8. Gromov, Asymptotic Invariants of Infinite Discrete Groups
9. de la Harpe, Topics in Geometric Group Theory
10. Lyndon and Schupp, Combinatorial Group Theory
11. Meier, Groups, Graphs and Trees: An Introduction to the Geometry of Infinite Groups
12. Rotman, An introduction to the theory of groups

1. Problems in Geometric Group Theory Wiki
2. Baumslag, Myasnikov and Shpilrain, Open Problems in combinatorial and geometric group theory
3. Baumslag, Problem areas in Infinite Group Theory for Finite Group Theorists, Proceedings of Symposia in Pure Mathematics Volume 37, 198
4. Open Problem Garden
5. The Kourovka Notebook (No. 18, 2014)