This is an expository talk based on the first half of the Temperley-Lieb-Jones Theories chapter of Zhenghan Wang's monograph "Topological Quantum Computation". In it, we will define the Temperley-Lieb algebra, become familiar with its properties as a diagrammatic algebra and ultimately define the Jones-Wenzl projectors (or idempotents). Understanding this algebra, and in particular, these projectors, is essential for topological quantum computation.