Introduction to $F$-isocrystals on the line

We will review basic properties of $F$-isocrystals on a smooth variety, with particular attention to the case of an open subset of the projective line. Topics: convergence conditions, Dwork's trick, the slope filtration, and the local monodromy theorem and its applications. If time permits we will discuss Lauder's work on the explicit computation of Frobenius matrices, and Katz's congruence formulas for the Frobenius of a curve.