(Topics) Lattices, basic theory of Universal Algebra, Latin Squares, Boolean Algebras, connections with Model Theory, recent developments and open problems.

(Topics) Algebraic sets, Algebaic varieties, Local study: tangent spaces/tangent cones/singularities, Projective varieties, Finite maps, Dimension theory, Regular maps and their fibres, Algebraic geometry over an arbitrary field, Divisors and intersection theory, Sheaves, Differentials, Algebraic varieties over the complex numbers.

(Topics) Module Theory, Divisibility and UFDs, Noetherian and Artinian Modules, Localization, Projective/Injective/Flat Modules, Tensor Products, Basic Field Theory.

(Topics)Groups, Rings, Fields, Modules, More Group Theory (e.g. Sylow's theorems), Galois theory, Algebraic Number Theory, Algebraic Geometry, Noncommutative Algebra, Homological Algebra. Includes written solutions to exercises.

(Topics) Groups, Rings, Matrices and Matrix Rings, Linear Algebra. (Emphasis on integrating linear algebra with abstract algebra.)