Infinity categories, as formulated by André Joyal and developed by Jacob Lurie, have become a useful framework for dealing with higher categorical phenomena in different areas, including representation theory and algebraic geometry. The goal of this talk is to introduce just enough background on simplicial homotopy theory to define infinity categories, including the prerequisites to read the first chapter of Lurie's book, Higher Topos Theory. If time allows, we will discuss basic properties and examples of infinity categories.