What is Mean–variance optimisation, risk-aversion parameter, efficient frontier?

Mean–variance optimisation chooses the weights $w$ that maximise $\alpha^\top w - \frac{\gamma}{2} w^\top\Sigma w$ subject to constraints, for an alpha forecast $\alpha$ and a covariance forecast $\Sigma$ over the same horizon (Markowitz, 1952). The risk-aversion parameter $\gamma$ sets the trade between expected return and variance. The efficient frontier is the set of portfolios, over all $\gamma$, with the highest expected return for their risk.