Books
General texts
[DuFo04], chapters 1–14 (groups, rings, modules and vector spaces, fields and Galois theory) and 18–19 (representation and character theory)
Groups, rings, and modules: Cambridge Part IB lecture notes
Galois theory: Cambridge Part II lecture notes
Representation theory
Serre, Linear Representations of Finite Groups, sections 1–6.
Fulton and Harris, Representation Theory: A First Course; chapters 7–10 treat Lie groups and Lie algebras.
Notes
Review of definitions and theorems
Amherst algebra qualifying-exam study guide
Abstract algebra test review: direct products and quotient groups
Tevelev, Graduate Algebra: Numbers, Equations, Symmetries – graduate algebra notes covering field extensions and Galois theory, radicals and cyclotomic fields, quadratic extensions and reciprocity, affine algebraic geometry and the Nullstellensatz, localization and Nakayama’s lemma, and representations and characters of finite groups. The notes include exercise sections and sample midterms.
MIT algebra qual preparation page