Isolated singularities of holomorphic functions: their classification, Laurent series, meromorphic functions, and the behavior near an essential singularity.
Classifying a singularity, the limit, boundedness, and Laurent series criteria.
Laurent series, the expansion on an annulus.
Removable singularities, poles, essential singularities, statements and proofs for each kind.
Meromorphic functions, functions whose singularities are poles.
Casorati-Weierstrass and Picard, the values taken near an essential singularity.