You should start with the general definition of Reinforcement Learning problem. And what Markov Decision Process is.
DQN, A3C, PPO and REINFORCE are algorithms for solving reinforce learning problems. These algorithms have their strengths an weaknesses depending on the details of the underlying problem.
Multi-Armed Bandit is not even an algorithm - it is as subclass of reinforcement learning problems, where your environment (usually) doesn't have any state transitions and your actions are just a single choice from (usually) fixed and finite set of choices.
Multi-Armed Bandit is used as an introductory problem to reinforcement learning, because it illustrates some basic concepts in the field: exploration-exploitation tradeoff, policy, target an estimate, learning rate and gradient optimization. All these concepts are basic vocabulary in RL. I recommend reading (and, very importantly, doing all the exercises) the Sutton and Barto book chapter two to get familiarized with it.