In this diploma thesis, we explore chaos in discrete dynamical systems. First, we define dynamical systems in general and introduce an iterated map as the prototypical example of a discrete dynamical system. We describe the three conditions that define chaotic discrete dynamical systems: sensitive dependence on initial conditions, dense periodic points and topological transitivity. Then, we examine the dynamics of the one-parameter family of tent maps $T_\mu$ where $\mu > 0$ and show that the dynamic system arising from iterating $T_\mu$ is chaotic for some parameters $\mu$. For $\mu = 2$, we directly check that the system meets criteria for chaotic systems. For $\mu > 2$, we introduce the symbol space $\Sigma_2$ and show that the shift map $\sigma$ is chaotic. We then define a map that is a topological conjugacy between $T_\mu$ and $\sigma$ and show that it preserves chaoticity.
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