Recent Developments and Resources
Bibliography and Further Reading Guide
A guide to the source's bibliography and to the standard references for the subject, organised by what each is for.
Learning objectives
- Navigate the source's own bibliography structure
- Identify the standard modern references
- Select reading appropriate to a given goal
The source's bibliography
The source carries a two-part bibliography on book pages 291–302: a list of books, and a list of research papers. It is comprehensive for the subject as of around 1981 and remains a useful guide to the classical literature.
- Books section
- book pages 291–293
- Research papers section
- book pages 293–302
- Author index
- book pages 303–305
- Subject index
- book pages 306–314
Standard references for the subject
| Work | Scope | When to use |
|---|---|---|
| Burris and Sankappanavar, A Course in Universal Algebra (1981; Millennium Edition) | Introductory and comprehensive | First systematic course; the source of this collection |
| Grätzer, Universal Algebra (2nd ed. 1979) | Comprehensive reference | Detailed treatment of lattices and free algebras |
| McKenzie, McNulty and Taylor, Algebras, Lattices, Varieties (1987; reissued 2018) | The standard modern reference | Deeper and more current than the source; the natural next text |
| Hobby and McKenzie, The Structure of Finite Algebras (1988) | Tame congruence theory | The classification of locally finite varieties |
| Freese and McKenzie, Commutator Theory for Congruence Modular Varieties (1987) | Commutator theory | The theory anticipated by the source's §13 |
| Clark and Davey, Natural Dualities for the Working Algebraist (1998) | Duality theory | The generalisation of Stone duality |
| Bergman, Universal Algebra: Fundamentals and Selected Topics (2011) | Modern introduction | An alternative first course |
Adjacent subjects
| Area | Standard reference |
|---|---|
| Lattice theory | Grätzer, Lattice Theory: Foundation (2011) |
| Model theory | Hodges, Model Theory (1993); Chang and Keisler, Model Theory (3rd ed. 1990) |
| Boolean algebras | Koppelberg, Handbook of Boolean Algebras Vol. 1 (1989) |
| Stone duality and topology | Johnstone, Stone Spaces (1982) |
| Clone theory | Szendrei, Clones in Universal Algebra (1986) |
| Constraint satisfaction | Barto, Krokhin and Willard, survey articles on the algebraic approach |
Reading by goal
A working knowledge
This collection's Orientation, Lattice and Core streams, alongside the source's Chapters I and II. Then Bergman or the source's short course.
Research preparation
The source in full, then McKenzie, McNulty and Taylor. Add Hobby and McKenzie for finite algebras and Freese and McKenzie for the commutator.
Algebraic logic
The source's Chapter IV, then Clark and Davey for dualities and the cylindric algebra literature.
Computer science applications
The source's Chapter III, then the constraint satisfaction survey literature and Eilenberg for automata.
The Millennium Edition is a corrected re-typesetting of the 1981 Springer GTM 78 text, prepared by the authors. Its mathematical content follows the original; pagination differs from the Springer printing, so citations should specify which edition is meant. This collection cites the Millennium Edition throughout.
Frequently asked questions
Is the source still the best first text?
It remains one of the standard choices, and its availability makes it widely used. Bergman's book is a more recent alternative covering similar ground with some later developments included.
What should be read after this collection?
McKenzie, McNulty and Taylor is the natural next step — it covers the same foundations in more depth and continues into material developed after the source was written.
Source. S. Burris and H. P. Sankappanavar, A Course in Universal Algebra, The Millennium Edition — a corrected re-typesetting of Springer-Verlag Graduate Texts in Mathematics 78 (1981). Section Bibliography, book pages 291-302.
This page is an original exposition prepared for the KEVOS® knowledge library. It restates and reorganises mathematical results; it is not a reproduction of the source text.