The text discusses the mathematical framework for designing Reinforcement Learning (RL) algorithms. It begins by defining the problem setting, including the observation space, action space, reward function, and terminal condition. The goal of RL algorithms is to learn a policy that maximizes the total rewards within an episode, but there is a chicken-and-egg problem since the agent needs to see future returns to act on the environment. To overcome this, RL agents form an estimate of what they think will be in the future if they act according to their current policy, leading to the concept of expectation. The main goal of RL algorithms is to learn a policy that achieves the maximum expected returns in its environment. The RL loop involves observing the world, acting on it, and receiving a reward, with the agent updating its policy using collected data to maximize rewards. A discount factor is introduced to prioritize near-term rewards and set the length of the time horizon for maximizing rewards. The framework is very general, allowing for the design of various RL algorithms without making assumptions about the underlying problem.