What is Black–Scholes model?

The Black–Scholes model is a market with a bank account growing at a constant rate $r$ and a share that pays a continuous dividend yield $q$ and follows a geometric Brownian motion (One Quant Book 4, chapter 4) under the real-world measure,

with constant $\mu$ and $\sigma>0$. Trading is continuous and frictionless, short sales are allowed, and cash can be borrowed and lent at $r$.