First Lecturer (Chris): Define a cell (or CW) complex along with the n-skeleton, the dimension of cell complex (if finite dimensional), and the Euler characteristic of a (finite) cell complex (p.6, you do not need to talk about the house with 2 rooms, you also do not need to prove that the Euler characteristic is a "homotopy invariant"). Then define orientable surfaces of genus g as identification spaces, drawing lots of pictures. Point out that the orientable surfaces have a cell structure with 1 0-cell, 2g 1-cells and 1 2-cell. Give the cell structure for Sn and a graph.
Second Lecturer (Collin): Explain Example 0.4: Define RPn as space of lines in Rn+1. Then show that RPn is a quotient space of Sn, identifying antipodal points. Then show how this gives RPn a cell structure with 1 cell in each dimension up to n. Define a subcomplex of a cell complex and a CW pair. Show that RPk is a subcomplex of RPn for k ≤ n. Define CPn. State (without proof) that CPn has a cell structure with 1 cell in even dimensions up to 2n.