Jan Schröer
FDAtlas

FDAtlas (09.09.21)
Atlas of finitedimensional algebras (313 pages, everything in one file).
Chapters of Part 1 of the FDAtlas:

Representationfinite algebras
directed, distributive, representationfinite (representationinfinite),
standard (nonstandard)

Tame and wild algebras
τtame, derived tame,
generically tame, tame (ndomestic, domestic, linear growth, polynomial growth, exponential growth), wild (strictly wild, controlled wild, endo wild, controlled endo wild, WILD, strictly WILD)

Hereditary algebras
hereditary, path, preprojective,
quasihereditary, Schur, semisimple, separable, species, strongly quasihereditary

Tilted algebras
τtilting finite, nAuslander, nCY tilted, nhereditary, nrepresentationfinite, almost hereditary, Auslander, canonical, concealed, concealed canonical, fractionally CY, Jacobian, quasicanonical, quasitilted, shod,
tilted, tubular, twisted fractionally CY, weakly nrepresentationfinite (nrepresentationinfinite), weakly shod

Selfinjective algebras
Brauer graph, Brauer tree, Frobenius, group, Hopf, periodic, repetitive, selfinjective, symmetric,
trivial extension, twisted periodic, weakly symmetric

Gorenstein algebras
nGorenstein, IwanagaGorenstein, QF3,
weakly Gorenstein

Biserial algebras
biserial, clannish, gentle, Nakayama, skewedgentle, special biserial, string

Multiplicative basis algebras
incidence
locally hereditary, monomial, multiplicative basis (multiplicative Cartan basis, filtered multiplicative basis)

Graded algebras
differential graded, enveloping, Ginzburg dg, graded, Hochschild cohomology, Koszul, Koszul dual, quadratic, tensor, Yoneda

Other algebras
Pmaximal, Pminimal, gendosymmetric, local,
lowdimensional, Nagase Pminimal, onepoint extension, tree, triangular
The representation theory of finitedimensional
algebras is a relatively young area of mathematics.
Its big bang or rather big bangs were Gabriel's classification of
representationfinite quivers in 1970 and Auslander and Reiten's
discovery of almost split sequences (aka AuslanderReiten sequences) in 1975.
There is quite a large zoo of classes of finitedimensional algebras which people study for various reasons.
Many of these classes have a beautiful representation theory and often provide a link to other areas of mathematics or mathematical physics.
Part 1 of the FDAtlas is a compilation of short notes on the most important
classes. (I identified about 100 of these up to now.) Usually, I will briefly define a class, give some examples, mention a few important results, and provide literature recommendations for
further reading.
Part 2 contains a recollection of some fundamental results and techniques from the representation theory of finitedimensional algebras.
This includes an overview of the categories and subcategories which are frequently studied.
I also give a list of general conjectures, e.g. the classical homological conjectures. Many more conjectures can be found in the various more specialized sections of Part 1.
There will be regular updates.