How much algebra one needs to study algebraic topology and homotopy theory?

Question

I wonder how much algebra(group theory, abstract algebra, linear algebra, ring theory, field theory) is assumed as a prerequisite in most of the modern algebraic topology text. For example, these

J.Strom "Modern Classical Homotopy Theory"

Tammo tom Dieck "Algebraic Topology"

P.May "A Concise Course in Algebraic Topology.