What is Backpropagation, mini-batch, epoch?

Backpropagation computes the gradient of the loss with respect to every parameter of a network by reverse-mode algorithmic differentiation (Book 4, chapter 28): one forward pass stores the layers’ values, one backward pass propagates $\partial\mathcal L/\partial z_l$ from the output to the input. A mini-batch is the random subset of training rows on which one gradient step is computed; an epoch is one pass over the training set in mini-batches.