This talk will take place on Zoom. Please contact ciappara@maths.usyd.edu.au for the link or to be added to the Seminar’s mailing list. Abstract: The talk will closely follow the first chapter of Hatcher’s book on topological K-theory. To begin, we will motivate vector bundles and give an overview of the Seminar’s theme this semester. We will then cover foundational definitions, terminology, and standard examples from topology, including vector bundles on spheres and tangent bundles associated to smooth manifolds. Sections of bundles and standard constructions such as direct sums, inner products, and tensor products will also be discussed. Time: 10 am -- 11:20 am, 21 August Seminar website: https://www.maths.usyd.edu.au/u/ciappara/SAS.html