Explore the intricacies of tropical geometry in this third lecture on the geometry of tropical varieties and their applications. Delve into key concepts such as fans, fanfolds, tropical fans, and tropical fanfolds, with illustrative examples provided. Learn about operations and constructions on tropical fans and fanfolds, including products and star subdivisions. Examine divisors on tropical fans, their construction, and the concept of principal divisors. Investigate tropical modifications and their properties through propositions. Discover the importance of shellability for tropical fans and fanfolds, supported by examples and theorems. Engage with the material through a Q&A session at the end of this comprehensive 1-hour 9-minute lecture presented by Omid Amini at the International Centre for Theoretical Sciences.