Section 2 begins by considering the simplest case of a diffraction grating, a single, infinitesimally narrow slit. The purpose of this section is to introduce the primary concepts and approximations used in the later sections. If you are happy accepting Eq. 8 on faith, you can skip Section 2 and begin directly with Section 3.2.
Section 3 studies the phenomenon of interference, which happens in cases where there are more than one slit. The central result of these notes is the N-slit diffraction pattern (Eq. 17) from this section. From this equation, one may understand the two slit pattern (N=2) as a special case, or deal with any larger number of slits. In fact, from this one result, one may also understand the pattern for a single slit of finite width (Section 4) and for the more complex case of N slits of finite width (Section 5).