There is no magic in a neural network — only three ideas composed together. Work through them in order: what a non-linearity buys you, how gradient descent uses a slope, and how backpropagation gets every gradient in one backward sweep. Then go further: attention, and the Transformer built from it, following the original paper step by step, today's large language models, and how small LLMs are made good with distillation, pruning and quantization. Every page computes its numbers live.