I'm working on Eilenberg-Mac Lane spaces and I'm reading this article in ncatlab. First, in Hatcher, a homotopy type is simple a homotopy equivalence, i.e, two spaces $X$ and $Y$ has the same homotopy type iff there exists a homotopy equivalence $f: X \to Y$. But, we can make this definition more weaker just saying that $f$ is a weak homotopy equivalence ($f$ induces a isomorphism on the (absolute) homotopy groups for all $n$). In definition of ncatlab, $X$ and $Y$ has the same homotopy 1-type if they are linked by a zig-zag chain of homotopy 1-equivalences, i.e $f$ induces isomorphism on $\pi_0$ and $\pi_1$. But, this articles cites no references. The classifications of $1$-type seems to me like the definition of Eilenberg-Mac Lane spaces
Where can I find references of this subject? articles or books thats clarifing this definitions and algebraic classifications of homotopy 1-types?