The study of operations and the structures they generate, from groups to categories of modules.
14 topics · 18 curated works
No prior grounding assumed.
Abstract Algebra: Theory and Applications
Thomas W. Judson · 1997
Introduces groups, rings and fields through worked computational examples first, treating abstract structure as something proof grows out of rather…
+3 more at this level
Assumes you know the vocabulary.
A Course in Universal Algebra
Stanley Burris & H.P. Sankappanavar · 1981
Treats groups, rings and lattices as instances of one object, the algebra of a given signature, and argues Birkhoff's HSP theorem is the fact that…
+3 more at this level
Primary sources and full treatments.
Lehrbuch der Algebra
Heinrich Weber · 1895
A comprehensive three-volume survey of algebra as understood at the close of the nineteenth century — equations, groups, fields and Galois theory…
+9 more at this level
12 of 18 works
Thomas W. Judson
Introduces groups, rings and fields through worked computational examples first, treating abstract structure as something proof grows out of rather than starts from.
link checked 17 Sept 2026Brian C. Hall
Builds Lie groups and Lie algebras entirely out of matrices before introducing any manifold theory, arguing the exponential map and its bracket are already accessible with the linear algebra a reader has.
link checked 17 Sept 2026Grant Sanderson (3Blue1Brown)
Builds linear algebra from geometric intuition first, so matrices become transformations rather than grids of numbers.
≈2 hourslink checked 17 Sept 2026Grant Sanderson (3Blue1Brown)
Introduces abstract groups through the symmetries they preserve rather than the objects that carry them, and uses the classification of finite simple groups to explain why the Monster group's existence was itself a discovery.
link checked 17 Sept 2026Stanley Burris & H.P. Sankappanavar
Treats groups, rings and lattices as instances of one object, the algebra of a given signature, and argues Birkhoff's HSP theorem is the fact that makes a single theory of varieties possible across all of them.
link checked 17 Sept 2026Charles A. Weibel
Traces how the notion of a derived functor emerged independently from algebraic topology and module theory, arguing the two were the same idea before anyone noticed.
link checked 17 Sept 2026Gilbert Strang (MIT OpenCourseWare)
Teaches linear algebra from the column space outward — a matrix is what it does to vectors, and the four fundamental subspaces explain every solvability question that follows.
link checked 17 Sept 2026Pavel Etingof et al.
Builds representation theory of finite groups and quivers around worked examples and problems from an MIT course, introducing category-theoretic language only once it is actually needed.
link checked 17 Sept 2026Heinrich Weber
A comprehensive three-volume survey of algebra as understood at the close of the nineteenth century — equations, groups, fields and Galois theory built up systematically — and the last major textbook of the field before the axiomatic reforms of the next generation redefined it.
600 pageslink checked 17 Sept 2026William Burnside
Systematises everything then known about finite groups — Sylow subgroups, solvable and simple groups, transitive permutation groups — into the first English-language textbook on the subject.
link checked 17 Sept 2026Leonard E. Dickson
Treats algebras as abstract structures defined by their multiplication tables rather than as number systems, and classifies them by that structure — an early statement of the algebraic method itself.
link failing as of 17 Sept 2026Emmy Noether
Introduces the ascending chain condition as the defining property of what are now called Noetherian rings, refounding ideal theory on axioms rather than on number fields.
link checked 17 Sept 2026