You should start with the general definition of [Reinforcement Learning][1] problem. And what [Markov Decision Process][2] 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][3] 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][4] chapter two to get familiarized with it. 
  

[1]:https://en.wikipedia.org/wiki/Reinforcement_learning
[2]:https://en.wikipedia.org/wiki/Markov_decision_process
[3]:https://en.wikipedia.org/wiki/Multi-armed_bandit
[4]:http://incompleteideas.net/book/the-book.html