Inverse limit, Completion and Properties of Completion.

Hilbert series of graded modules, Hilbert-Samuel polynomial of a module, Dimension Theory, System of

Flat and faithfully flat modules, Complexes, Homology and Cohomolgy, Projective resolution and
injective resolution, Tor and Ext, Projective dimension, injective dimension and global dimension.

Regular sequences and Koszul complex, Depth, Cohen-Macaulay rings and modules, Regular local