Lecture Notes of Courses (.ps and .pdf files)
This is a first course in number theory. It includes p-adic numbers.
This course is an introduction to modules over rings, Noetherian modules, unique factorization domains and polynomial rings over them, modules over principal ideal domains, localization.
This course (40 hours) is a relatively elementary course which requires minimal prerequisites from Commutative Algebra (see above) for its understanding.
Following an algebraic prerequisited review part, integral structures, Dedekind rings, splitting of maximal ideals in field extensions, finiteness of the ideal class group and Dirichlet's theorem on units are treated next, p-adic numbers and class field theory for the field of rational numbers are introduced in the last part of the course.
This is a very short introduction to homological algebra
This course (25 hours) presents categories, functors, chain complexes, homologies, free, projective and injective obejcts in the category of modules over a ring, projective and injective resolutions, derived functors, Tor and Ext, cohomologies of modules over a finite group, restriction and corestriction.
This is a very short introduction to local fields and local class field theory
which uses an explicit description of the local reciprocity homomorphism
and its inverse and does not use Galois cohomology and the Brauer group.
See also 10 magic lectures on local fields .