We will cover part of the book on Geometric Approximation Algorithms by Sariel Har Peled (AMS 2011).
Chapter 2. Quadtrees – Hierarchical Grids, Tamar Lavee
Chapter 3. Well Separated Pair Decomposition, Eyal Altshuler
Chapter 4. Clustering, Ariel Persico
Chapter 5. On Complexity, Sampling, and epsilon-nets, and eplison-samples, Yuval Snappir
Chapter 6. Approximation via Reweighting, Eran Kravitz
Chapter 7. Yet Even More on Sampling (skip)
Chapter 8. Sampling and the moment technique, Dima Blokh
Chapter 9. Depth Estimation via Sampling, Eliad Zfadia
Chapter 10. Approximating the Depth via Sampling and Emptiness, Adi Vardi
Chapter 11. Random Partition via Shifting, Tomer Margalit
Chapter 12. Good triangulations and meshing, Ofer Rothschild
You can find the full table of contents and some early version of the book here. But please use the most recent version for preparing your presentation.