k-theory is a valuable tool with applications in various areas of mathematics, including topology, geometry, algebraic geometry, and number theory. in this talk i will attempt to give a rough outline of what k-theory is about, in the algebraic as well as the geometric context. given a ring r and a space x, i will define the groups k(r) and k(x), and explain the relation between the two. i also hope to outline some applications in various fields. this talk should be accessible and i hope interesting to 2022年亚洲世界杯预选赛 of both algebra and geometry alike.