I will give a gentle introduction to algebraic K-theory from the perspective of higher algebra. A useful approach for studying algebraic K-theory is through trace methods which provide maps from algebraic K-theory to invariants which are built from Hochschild homology and which are more amenable to calculations. In favorable situations, these invariants are good approximations to algebraic K-theory. In this talk, I will focus on a particular one of these invariants called TR. This is the analogue of crystalline cohomology in higher algebra, or more precisely an analogue of the de Rham?Witt complex. I will explain the connection between this invariant and Bloch?s curves on K-theory.