Define deformation retraction, do some examples (like a Mobius band and annulus def retract to a circle, their cores), define a homotopy of maps f0 and f1. Define a retract and show that this is not the same as deformation retract since every space X retracts to a point. Define a homotopy relative to a subspace (or relative homotopy), homotopy equivalence, and homotopy type. Show that if X deformation retracts onto A (A subspace of X) then X is homotopy equivalent to A (hence homotopy equivalence is a generalization of deformation retraction). [You do not need to talk about two spaces being h.e. (homotopy equivalent) iff there is another space Z.... (as in the last paragraph on p.3)]. Define when a space is contractible. Show that Rn is contractible. [You do not need to talk about the house with 2 rooms]. If there is time you can show why the spaces in either example 0.8 or 0.9 (p. 11-12) are homotopy equivalent.