Topological data analysis is a rapidly growing field at the intersection of data science and algebraic topology that considers the shape of data. Starting with large and complex data sets, a manageable topological space can be constructed through known relationships amongst the data; studying features of this space corresponds to studying patterns in the data. Before tools from topological data analysis can be applied, concepts from algebraic topology must supply rigor to the aforementioned constructions and give us methods of discerning fundamental characteristics of them. We begin this talk with a motivating example that provides an overview of topological data analysis. Then we will learn about simplices, the building blocks of our constructions, how they can be used to define the homology groups of a topological space, what information homology groups encode, and explore examples particular to topological data analysis. This talk is intended to give anyone interested in topological data analysis, the tools to begin learning more and is written with few assumptions in mind.