@unutbu's link in the comment is a good introductory read.
Solid understanding for AlphaZero most likely require a quantitative degree (PhD?). Are you asking for a crash course in AlphaZero?
Please note unless you invest significant amount of your time, nothing I say will work. There is no book that can possibly cover everything. You will need to work very hard.
Let's give a try. Crash course for AlphaZero.
1. Basic understanding in machine learning
Countless number of books. But if you don't have time, I'd recommend Professor Andrew Ng's machine learning courses on Coursera.
Your keywords: training sets, test sets, stochastic gradient descent, learning rate, GPU, cost function, cross entropy.
2. Deep neutral networks
You need to understand about neural networks. I'd recommend Professor Ian Goodfellow's deep learning book if you're serious. If you don't have time, please again follow Professor Andrew Ng 's online course on Coursera. You don't have to go though all chapters (but you should!).
YouTube has many quick introduction to neural networks, try them.
Your keywords: neuron, layers, weights, bias, mini-batch, activation.
3. Monte Carlo Tree Search
You should understand what Monte Carlo is. Books about Monte Carlo is everywhere on Amazon. Read the wikipedia about MCTS if you don't have time.
Your keywords: sampling, expansion, simulation, rollouts, backpropagation.
3. Reinforcement learning
Your keywords: policy gradient, gradient descent, learning rate
5. Chess board representation
The paper itself is simplest. The model encodes the board state (e.g. pieces) as a series of one-hot encoding binary values.
6. MCTS vs alpha-beta