William Adkins/Steven Weintraub: Algebra. An approach via module theory.
Springer 1992, 530p. 3-540-97839-9. DM 92.

Michael Artin: Algebra. Birkhaeuser 1993, 720p. 3-7643-2927-0.

John Beachy: Abstract algebra II. 1996, 160p.

John Beachy/William Blair: Abstract algebra.
Waveland Press 1996, 430p. 0-88133-866-4.

Abstract Algebra II, by John A. Beachy 
Copyright 1996, 160 pages 

21788 Siegfried Bosch: Algebra. Springer 2003, 350p. Eur 32.

26484 Dietrich Burde: Algebra im Überblick. Internet 2011, 82p.
Elementary algebra and coding theory.

P. Cameron: Introduction to algebra. Oxford UP 1998, 300p. Pds. 17.
"... standard topics of ring, field and group theory ... modules
... normal forms of matrices (over arbitrary fields) ... coding theory
and Galois theory ... at least glimpses to more advanced topics are
given, e.g. on finite simple groups, group extensions and homological
algebra, algebraic geometry, universal algebra and category
theory. Altogether this is a concise but solid introduction into
algebra and linear algebra." (G. Kowol)

23147 Andrea Caranti: Note per un corso di Algebra. Internet 2012, 165p.

3516 Claude Chevalley: Concetti fondamentali di algebra. Feltrinelli 1980.

L. Childs: A concrete introduction to higher algebra.
Springer 1992, 340p. DM 90.

11615 G. Chrystal: Algebra. 2 volumes. Chelsea.

Johann Cigler: Körper - Ringe - Gleichungen.
Spektrum 1995, 310p. 3-86025-679-3. DM 48.

P. Cohn: Basic algebra. Springer 2003, 470p. Eur 65.
Groups, rings, fields, quadratic forms (also in characteristic 2).

P. Cohn: Further algebra and applications. Springer 2003, 450p. Eur 80.
Universal algebra and ultraproducts, basic homological algebra, groups
and algebras, special classes of rings, some applications.

16966 David Dummit/Richard Foote: Abstract algebra. Wiley 2004, 930p. $113.
"Now as before, this excellent textbook on modern abstract
algebra is extremely comprehensive, versatile, didactically
pronounced, mathematically rigorous, conceptually and methodically
up-to-date, masterly composed and clearly written.
... unique features that make this (meanwhile classic) text a true
marvel, namely the unflagging lucidity and fullness, the cultured
and vivid exposition, the great flexibility for students and
instructors wishing to pursue a number of important areas of modern
algebra, the authors' hints for doing so, the rigorous and carefully
thought-out proofs, the encouraging ease in explaining also the
more advanced topics, and the wealth of material to choose from.
... the book under review is one of the greatest textbooks in
modern mathematics ..." (W. Kleinert)

Fine/Gaglione/Rosenberger: Introduction to abstract algebra.
Johns Hopkins UP 2014, 580p. Eur 71.

I. Gelfand/A. Shen: Algebra. 
Birkhaeuser 1993, 160p. 3-7643-3677-3 (pb). SFR 36.

L. Gerritzen: Grundbegriffe der Algebra. Vieweg 1994, 140p. DM 34.
"Neben dem ueblichen Stoff (bis zum Hauptsatz der Galoistheorie) werden 
wichtige Ergaenzungen hehandelt (wie z.B. topologische und Liegruppen), sowie 
wichtige Algebren (Tensoralgebra, Grassmann-Algebra, Symmetrische Algebra), 
Derivationen und Differentiale (universeller Differentialmodul, 
De-Rham-Komplex), Schemata (mit Beweis des Hilbertschen Nullstellensatzes, 
sowie eine Einfuehrung in die homologische Algebra (mit Cech-Kohomologie))." 
(Harald Rindler).

22560 Roger Godement: Cours d'algebre. Hermann 2005, 670p. Eur 33.

M. Hazewinkel (ed.): Handbook of algebra I. North-Holland, ca. 1995.

M. Hazewinkel (ed.): Handbook of algebra II.
North-Holland, ca. 1995, 880p. $178.

T. Hungerford: Algebra. Springer 1974. 3-540-90518-9. DM 102.

J. Jantzen/J. Schwermer: Algebra. Springer 2005, 340p. Eur 25.

C. Karpfinger/K. Meyberg: Algebra. Akad. Verlag 2009, 350p.

G. Kempf: Algebraic structures. Vieweg 1995, 160p. 3-528-06583-4. DM 42.
A good book which covers classical algebra and introduces to many other
attractive subjects as Lie algebras, Clifford algebras, dimension of
commutative rings, Tor.

Otto Koerner: Algebra. Adademische Verlagsgesellschaft 1974.

Ernst Kunz: Algebra. Vieweg 1991, 250p. 3-528-07243-1. DM 36.
Ein gegluecktes Lehrbuch der Algebra.

Serge Lang: Undergraduate algebra. 
Springer 1990, 370p. 3-540-97279-x. DM 87.

N. Lauritzen: Concrete abstract algebra - from numbers to Gröbner bases.
Cambridge UP 2003, 240p. Pds 20.

Rudolf Lidl/Harald Niederreiter: Finite fields and their applications.
In Hazewinkel, ca. 1995.

Rudolf Lidl/Günter Pilz: Applied abstract algebra.
Springer 1998, 490p. 3-540-98290-6. DM 88.

25822 Falko Lorenz: Einführung in die Algebra II. Spektrum 1997, 390p. Eur 30.

25821 Falko Lorenz/Franz Lemmermeyer: Algebra 1. Spektrum 2007, 390p. Eur 30.

Claudia Menini/Freddy van Oystaeyen: Abstract algebra. Dekker 2004, 620p. $95.

K. Meyberg: Algebra. 2 volumes. Hanser 1975. Should be a good textbook.

Giulia Maria Piacentini Cattaneo: Algebra. Decibel 1996.

19246 Friedrich Pillichshammer: Einführung in die Algebra und diskrete
Mathematik. Internet 2006, 117p.

Günter Pilz: Algebra. Ein Reiseführer durch die scho''nsten Gebiete.
Universita''tsverlag Trauner (Linz).

1799 Hans-Joerg Reiffen/Guenter Scheja/Udo Vetter: Algebra. 

D. Robinson: An introduction to abstract algebra. De Gruyter 2003, 280p. Eur 43.

Joseph Rotman: Advanced modern algebra. AMS 2010, 1010p.

1589 Guenter Scheja/Uwe Storch: Lehrbuch der Algebra. 3 volumes. Teubner. 
First volume: 1994 (new edition, contains also the old third volume), 700p. 
3-519-12203-0. DM 62.                                              
Second volume : 1988, 810p. 3-519-02212-5. DM 68. 
The third volume (1981, 240p. 3-519-02223-0. DM 28.) is contained in the new 
edition of the first volume. Very complete, many exercises.

11533 J. Serret: Cours d'algebre superieure. 2 volumes.
Gauthiers-Villars 1928.

22809 Wolfgang Soergel: Algebra. Internet 2011, 660p.

27851 Fabio Stumbo: Appunti di algebra. Univ. Ferrara 2019, 135p.

1590 B. van der Waerden: Algebra. 2 volumes. Springer 1966.

Heinrich Weber: Lehrbuch der Algebra. 3 volumes. Chelsea.

5840 Hans Zassenhaus: Methoden und Probleme der modernen Algebra.
Jber. DMV 96 (1994), 21-33. Zassenhaus' Antrittvorlesung von 1947 in Hamburg.