This document discusses sequences and series of functions. It defines pointwise and uniform convergence of sequences of functions. Pointwise convergence means the sequence converges for each value, while uniform convergence means the convergence is uniform across all values. Cauchy's criterion for uniform convergence is presented. Theorems are provided about uniform convergence implying continuity and uniform convergence of series if partial sums are bounded. The definition of uniform convergence on compact metric spaces using the supremum norm is also given.