Algebra: Introductory Surveys

Allenby, R.B.J.T. Rings, Fields and Groups: An Introduction to Abstract Algebra New York, NY: Edward Arnold, 1983.

** Artin, Michael. Algebra Englewood Cliffs, NJ: Prentice Hall, 1991.

Bhattacharya, P.B.; Jain, S.K.; and Nagpaul, S.R. Basic Abstract Algebra New York, NY: Cambridge University Press, 1986.

*** Birkhoff, Garrett and Mac Lane, Saunders. A Survey of Modern Algebra, New York, NY: Macmillan, 1965, 1977. Fourth Edition.

Burnside, William Snow and Panton, Arthur William. The Theory of Equations with an Introduction to the Theory of Binary Algebraic Forms, Mineola, NY: Dover, 1960. 2 Vols.

Burton, D. Abstract Algebra Dubuque, IA: William C. Brown, 1988.

* Childs, Lindsay. A Concrete Introduction to Higher Algebra New York, NY: Springer-Verlag, 1979.

Dean, Richard A. Classical Abstract Algebra New York, NY: Harper and Row, 1990.

* Fraleigh, John B. A First Course in Abstract Algebra, Reading, MA: Addison-Wesley, 1976, 1989. Fourth Edition.

** Gallian, Joseph A. Contemporary Abstract Algebra, Lexington, MA: D.C. Heath, 1986, 1990. Second Edition.

Goldstein, Larry J. Abstract Algebra: A First Course Englewood Cliffs, NJ: Prentice Hall, 1973.

* Herstein, I.N. Abstract Algebra, New York, NY: Macmillan, 1986, 1990. Second Edition.

Hillman, Abraham P. and Alexanderson, Gerald L. A First Undergraduate Course in Abstract Algebra, Belmont, CA: Wadsworth, 1973, 1988. Fourth Edition.

* Hungerford, Thomas W. Abstract Algebra: An Introduction Philadelphia, PA: Saunders College, 1990.

Kostrikin, A.I. Introduction to Algebra New York, NY: Springer-Verlag, 1982.

Lang, Serge. Undergraduate Algebra New York, NY: Springer-Verlag, 1987.

Marcus, Marvin. Introduction to Modern Algebra New York, NY: Marcel Dekker, 1978.

McCoy, Neal H. and Janusz, Gerald J. Introduction to Modern Algebra, Boston, MA: Allyn and Bacon, 1960, 1987. Fourth Edition.

Pinter, Charles C. A Book of Abstract Algebra New York, NY: McGraw-Hill, 1982.

Algebra: Constructive and Computational Algebra

Barbeau, Edward J. Polynomials New York, NY: Springer-Verlag, 1989.

Connell, Ian. Modern Algebra: A Constructive Approach New York, NY: Elsevier Science, 1982.

* Dobbs, David E. and Hanks, Robert. A Modern Course on the Theory of Equations Washington, NJ: Polygonal, 1980.

* Humphreys, J.F. and Prest, M.Y. Numbers, Groups, and Codes New York, NY: Cambridge University Press, 1989.

Mines, Ray; Richman, Fred; and Ruitenburg, Wim. A Course in Constructive Algebra New York, NY: Springer-Verlag, 1988.

Sims, Charles C. Abstract Algebra: A Computational Approach New York, NY: John Wiley, 1984.

Algebra: Applied Algebra

Birkhoff, Garrett and Bartee, Thomas C. Modern Applied Algebra New York, NY: McGraw-Hill, 1970.

* Dornhoff, Larry L. and Hohn, Franz E. Applied Modern Algebra New York, NY: Macmillan, 1978.

Laufer, Henry B. Discrete Mathematics and Applied Modern Algebra Boston, MA: Prindle, Weber and Schmidt, 1984.

* Lidl, Rudolf and Pilz, Gunter. Applied Abstract Algebra New York, NY: Springer-Verlag, 1984.

Lipson, John D. Elements of Algebra and Algebraic Computing Reading, MA: Addison-Wesley, 1981.

** Mackiw, George. Applications of Abstract Algebra New York, NY: John Wiley, 1985.

Algebra: Advanced Surveys

* Bourbaki, Nicolas. Elements of Mathematics: Algebra, New York, NY: Springer-Verlag, 1989, 1990. 2 Vols.

** Cohn, Paul M. Algebra, New York, NY: John Wiley, 1974, 1982. 2 Vols., Second Edition.

*** Herstein, I.N. Topics in Algebra, New York, NY: John Wiley, 1975. Second Edition.

* Hungerford, Thomas W. Algebra New York, NY: Springer-Verlag, 1974.

* Jacobson, Nathan. Lectures in Abstract Algebra, New York, NY: Springer-Verlag, 1953, 1975. 2 Vols.

*** Jacobson, Nathan. Basic Algebra I and II, New York, NY: W.H. Freeman, 1974, 1989. Second Edition.

Kostrikin, A.I. and Shafarevich, Igor R., eds. Algebra I: Basic Notions of Algebra New York, NY: Springer-Verlag, 1990.

* Lang, Serge. Algebra, Reading, MA: Addison-Wesley, 1965, 1984. Second Edition.

Ledermann, Walter and Vajda, Steven, eds. Algebra New York, NY: John Wiley, 1980. Handbook of Applicable Mathematics, Volume I.

*** Mac Lane, Saunders and Birkhoff, Garrett. Algebra, New York, NY: Chelsea, 1988. Third Edition.

*** van der Waerden, B.L. Algebra, New York, NY: Springer-Verlag, 1991. (Original title: Modern Algebra.)

Algebra: Group Theory

Aschbacher, Michael. The Finite Simple Groups and Their Classification New Haven, CT: Yale University Press, 1980.

** Budden, F.J. The Fascination of Groups New York, NY: Cambridge University Press, 1972.

* Burn, R.P. Groups: A Path to Geometry New York, NY: Cambridge University Press, 1985, 1987.

Conway, John Horton, et al. Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups New York, NY: Clarendon Press, 1985.

* Curtis, Charles W. and Reiner, Irving. Methods of Representation Theory with Applications to Finite Groups and Orders New York, NY: John Wiley, 1981.

* Curtis, Charles W. and Reiner, Irving. Representation Theory of Finite Groups and Associative Algebras New York, NY: John Wiley, 1962.

Dixon, J.D. Problems in Group Theory New York, NY: Blaisdell, 1967.

Feigelstock, S. Additive Groups of Rings Brooklyn, NY: Pitman, 1983.

Fuchs, L. Abelian Groups New York, NY: Academic Press, 1970.

* Gorenstein, Daniel. The Classification of Finite Simple Groups New York, NY: Plenum Press, 1983.

** Gorenstein, Daniel. Finite Simple Groups: An Introduction to Their Classification New York, NY: Plenum Press, 1982.

Grove, L.C. and Benson, C.T. Finite Reflection Groups, New York, NY: Springer-Verlag, 1985. Second Edition.

*** Hall, Marshall, Jr. The Theory of Groups, New York, NY: Chelsea, 1973. Second Edition.

Hall, Marshall, Jr. and Senior, J.K. Groups of Order $2^n(n eq 6)$ New York, NY: Macmillan, 1964.

Hill, Victor E. Groups, Representations, and Characters New York, NY: Hafner Press, 1975.

Johnson, D.L. Presentations of Groups New York, NY: Cambridge University Press, 1976.

* Kaplansky, Irving. Infinite Abelian Groups, Ann Arbor, MI: University of Michigan Press, 1969. Revised Edition.

* Kurosh, Alexander G. The Theory of Groups, New York, NY: Chelsea, 1960, 1970. 2 Vols., Second Edition.

** Ledermann, Walter. Introduction to Group Characters, New York, NY: Cambridge University Press, 1977, 1987. Second Edition.

*** Rotman, Joseph J. An Introduction to the Theory of Groups, Needham Heights, MA: Allyn and Bacon, 1965, 1984. Third Edition.

Scott, William R. Group Theory Mineola, NY: Dover, 1987.

Serre, Jean-Pierre. Linear Representations of Finite Groups New York, NY: Springer-Verlag, 1977.

Weinstein, Michael. Examples of Groups Washington, NJ: Polygonal, 1977.

* Weyl, Hermann. The Classical Groups: Their Invariants and Representatives Princeton, NJ: Princeton University Press, 1946.

Algebra: Rings and Ideals

Cohn, Paul M. Free Rings and Their Relations, New York, NY: Academic Press, 1985. Second Edition.

* Goodearl, K.R. and Warfield, R.B., Jr. An Introduction to Noncommutative Noetherian Rings New York, NY: Cambridge University Press, 1989.

* Herstein, I.N. Rings with Involution Chicago, IL: University of Chicago Press, 1976.

*** Herstein, I.N. Non-Commutative Rings Washington, DC: Mathematical Association of America, 1968.

* Jacobson, Nathan. The Structure of Rings, Providence, RI: American Mathematical Society, 1964. Revised Edition.

Jans, J. Rings and Homology New York, NY: Holt, Rinehart and Winston, 1964.

** Kaplansky, Irving. Fields and Rings, Chicago, IL: University of Chicago Press, 1969, 1974. Revised Second Edition.

Kostrikin, A.I. and Shafarevich, Igor R., eds. Algebra II: Non-Commutative Rings, Identities New York, NY: Springer-Verlag, 1991.

* Lambek, Joachim. Lectures on Rings and Modules, New York, NY: Chelsea, 1976. Second Edition.

* McConnell, J.C. and Robson, J.C. Noncommutative Noetherian Rings New York, NY: John Wiley, 1988.

McCoy, Neal H. Rings and Ideals Washington, DC: Mathematical Association of America, 1948.

McCoy, Neal H. The Theory of Rings New York, NY: Chelsea, 1973.

Passman, Donald S. The Algebraic Structure of Group Rings Melbourne, FL: Robert E. Krieger, 1985.

* Robinson, Abraham. Numbers and Ideals San Francisco, CA: Holden-Day, 1965.

Rowen, Louis Halle. Polynomial Identities in Ring Theory New York, NY: Academic Press, 1980.

* Rowen, Louis Halle. Ring Theory, New York, NY: Academic Press, 1988. 2 Vols.

* Sharpe, David. Rings and Factorization New York, NY: Cambridge University Press, 1987.

Small, Lance W. Noetherian Rings and Their Applications Providence, RI: American Mathematical Society, 1987.

Stenstrom, Bo. Rings of Quotients: An Introduction to Methods of Ring Theory New York, NY: Springer-Verlag, 1975.

Algebra: Fields and Galois Theory

* Adamson, Iain T. Introduction to Field Theory, New York, NY: Cambridge University Press, 1982. Second Edition.

* Artin, Emil. Galois Theory, Notre Dame, IN: University of Notre Dame Press, 1966. Second Revised Edition.

Brawley, Joel V. and Schnibben, George E. Infinite Algebraic Extensions of Finite Fields Providence, RI: American Mathematical Society, 1989.

* Edwards, Harold M. Galois Theory New York, NY: Springer-Verlag, 1984.

** Gaal, Lisl. Classical Galois Theory with Examples, New York, NY: Chelsea, 1973, 1988. Fourth Edition.

Garling, D.J.H. A Course in Galois Theory New York, NY: Cambridge University Press, 1986.

*** Hadlock, Charles R. Field Theory and Its Classical Problems Washington, DC: Mathematical Association of America, 1978.

Lang, Serge. Cyclotomic Fields I and II, New York, NY: Springer-Verlag, 1978--80, 1990. Second Edition.

* Lidl, Rudolf and Niederreiter, Harald. Introduction to Finite Fields and Their Applications New York, NY: Cambridge University Press, 1986.

* Lieber, Lillian R. Galois and the Theory of Groups: A Bright Star in Mathesis Brooklyn, NY: Galois Institute of Mathematics and Art, 1961.

* McCarthy, Paul J. Algebraic Extensions of Fields, New York, NY: Chelsea, 1976. Second Edition.

Rotman, Joseph J. Galois Theory New York, NY: Springer-Verlag, 1990.

*** Stewart, Ian. Galois Theory, New York, NY: Chapman and Hall, 1989. Second Edition.

Algebra: Commutative Algebra

** Atiyah, Michael F. and MacDonald, I.G. Introduction to Commutative Algebra Reading, MA: Addison-Wesley, 1969.

* Bourbaki, Nicolas. Elements of Mathematics: Commutative Algebra, New York, NY: Springer-Verlag, 1989.

Hutchins, Harry C. Examples of Commutative Rings Washington, NJ: Polygonal, 1981.

* Kaplansky, Irving. Commutative Rings, Boston, MA: Allyn and Bacon, 1974. Revised Edition.

Kunz, E. Introduction to Commutative Algebra and Algebraic Geometry New York, NY: Birkhauser, 1985.

Matsumura, Hideyuki. Commutative Ring Theory New York, NY: Cambridge University Press, 1986.

* Nagata, Masayoshi. Local Rings New York, NY: Interscience, 1962.

*** Zariski, Oscar and Samuel, Pierre. Commutative Algebra, New York, NY: Springer-Verlag, 1975, 1976. 2 Vols.

Algebra: Homological Algebra

Geramita, Anthony V. and Small, Charles. Introduction to Homological Methods in Commutative Rings Kingston: Queen's University Press, 1976.

* Hilton, Peter J. and Stammbach, U. A Course in Homological Algebra New York, NY: Springer-Verlag, 1971.

** Mac Lane, Saunders. Homology New York, NY: Springer-Verlag, 1963.

Northcott, D.G. A First Course of Homological Algebra New York, NY: Cambridge University Press, 1973, 1980.

** Rotman, Joseph J. An Introduction to Homological Algebra New York, NY: Academic Press, 1979.

Algebra: Category Theory

* Barr, Michael; and Wells, Charles. Category Theory for Computing Science Hemel Hemstead, UK: Prentice Hall International, 1990.

Blyth, T.S. Categories White Plains, NY: Longman, 1986.

* Herrlich, Horst and Strecker, George E. Category Theory: An Introduction, Berlin: Heldermann Verlag, 1979. Second Edition.

Lambek, Joachim and Scott, P.J. Introduction to Higher Order Categorical Logic New York, NY: Cambridge University Press, 1986, 1988.

** Mac Lane, Saunders. Categories for the Working Mathematician New York, NY: Springer-Verlag, 1971.

Pareigis, B. Categories and Functors New York, NY: Academic Press, 1970.

Algebra: Lie Algebras

Humphreys, James E. Introduction to Lie Algebras and Representation Theory New York, NY: Springer-Verlag, 1972.

* Jacobson, Nathan. Lie Algebras Mineola, NY: Dover, 1979.

* Kaplansky, Irving. Lie Algebras and Locally Compact Groups Chicago, IL: University of Chicago Press, 1971.

* Samelson, Hans. Notes on Lie Algebras New York, NY: Springer-Verlag, 1990.

Winter, David J. Abstract Lie Algebras Cambridge, MA: MIT Press, 1972.

Algebra: Universal Algebra

Burris, Stanley and Sankappanavar, H.P. A Course in Universal Algebra New York, NY: Springer-Verlag, 1981.

* Cohn, Paul M. Universal Algebra Norwell, MA: D. Reidel, 1981.

* Gratzer, George. Universal Algebra, New York, NY: Springer-Verlag, 1979. Second Edition.

Algebra: Special Topics

Artin, Emil. Geometric Algebra New York, NY: John Wiley, 1957.

* Bachmann, Friedrich; Schmidt, Eckart; and Garner, Cyril W.L. n-gons Toronto: University of Toronto Press, 1975.

Bass, Hyman. Algebraic $K$-Theory Redwood City, CA: Benjamin Cummings, 1968.

* Halmos, Paul R. Lectures on Boolean Algebras New York, NY: Springer-Verlag, 1974.

Meldrum, J.D.P. Near-rings and Their Links with Groups Brooklyn, NY: Pitman, 1985.

Monk, J. Donald and Bonnet, Robert, eds. Handbook of Boolean Algebras, Amsterdam: North-Holland, 1989. 3 Vols.

* Montgomery, Susan, et al., eds. Selected Papers on Algebra Washington, DC: Mathematical Association of America, 1977.

Sikorski, R. Boolean Algebras New York, NY: Springer-Verlag, 1960.

Silvester, John R. Introduction to Algebraic K-Theory New York, NY: Chapman and Hall, 1981.