A Brief Introduction to Algebraic K-theory

We give a brief survey of higher algebraic K-theory and its connection to motivic cohomology. We start with limits and colimits, and then pass to the combinatorial construction of topological spaces by means of “systems of simplices”, usefully mediated by simplicial sets. Definitions of K-theory are offered, and the main theorems are stated. A definition of motivic cohomology is offered and its major properties are listed. Many references to the literature are provided, especially for the development of motivic cohomology.