In this thesis, we explore the method of hypergraph containers and its applications to problems in extremal combinatorics and discrete geometry. We start by introducing containers on triangle-free graphs and use it to give a lower bound on the number of triangle-free graphs on n vertices. We then generalise to the container algorithm for independent sets in graphs, which is a version of regular graphs. The proof of this theorem is an algorithm. We study this algorithm and apply it to the Erdős-Rényi random graph G(n,p). After this we expand to hypergraphs, specifically 3-uniform hypergraphs. Finally we look at the application to a problem in discrete geometry: Given n points in the Euclidean plane ℝ², with at most three on any line, how large a subset are we guaranteed to find in general position (i.e., with at most two on any line)? A strong upper bound is obtained by using the hypergraph container method.