Explore advanced concepts in p-adic geometry through this comprehensive lecture focusing on topologies, diamonds, and the Fargues-Fontaine curve. Delve into the intricate world of p-adic mathematics as Judith Ludwig, an expert in the field, guides you through complex theoretical frameworks. Gain insights into the fundamental structures and properties of p-adic spaces, understand the significance of diamond structures in modern algebraic geometry, and unravel the mysteries of the Fargues-Fontaine curve. This in-depth presentation is ideal for mathematicians, researchers, and advanced students seeking to expand their knowledge in this specialized area of mathematics.