Basic algebraic topology in the amount covered by preceding course "Algebraic Topology" (and hence also all its prerequisites):
Basic group theory (up to the classification of finitely generated Abelian groups and notions of normal subgroups and conjugasy classes);
Basic linear algebra (rank of a linear operator, classification of quadratic forms...)
Basic analysis of functions of several variables (up to Implicit Function theorem and Taylor series),
Basic topology of subsets of Euclidean spaces (notions of closed, open, compact, connected sets, continuous functions and their topological properties).