Chapter 1 The Rank Invariant Stability via Interleavings

Chapter 2 Persistent Homology over Directed Acyclic Graphs

Chapter 3 A Complete Characterization of the One-Dimensional Intrinsic Čech Persistence Diagrams for Metric Graphs

Chapter 4 Comparing Directed and Weighted Road Maps

Chapter 5 Sweeping Costs of Planar Domains

Chapter 6 Scaffoldings and Spines: Organizing High-Dimensional Data Using Cover Trees, Local Principal Component Analysis, and Persistent Homology

Chapter 7 Density of Local Maxima of the Distance Function to a Set of Points in the Plane

Chapter 9 Cluster Identification via Persistent Homology and Other Clustering Techniques, with Application to Liver Transplant Data

Chapter 10 Pseudo-Multidimensional Persistence and Its Applications