  We survey Ozsv\'ath-Szab\'o's bordered approach to knot Floer homology. After
a quick introduction to knot Floer homology, we introduce the relevant
algebraic concepts ($\mathcal{A}_\infty$-modules, type $D$-structures, box
tensor, etc.), we discuss partial Kauffman states, the construction of the
boundary algebra, and sketch Ozsv\'ath and Szab\'o's analytic construction of
the type $D$-structure associated to an upper diagram. Finally we give an
explicit description of the structure maps of the $DA$-bimodules of some
elementary partial diagrams. These can be used to perform explicit computations
of the knot Floer differential of any knot in $S^3$. The boundary DGAs
$\mathcal{B}(n,k)$ and $\mathcal{A}(n,k)$ of [7] are replaced here by an
associative algebra $\mathcal{C}(n)$. These are the notes of two lecture series
delivered by Peter Ozsv\'ath and Zolt\'an Szab\'o at Princeton University
during the summer of 2018.
