  We provide a fairly self-contained account of the localisation and cofinality
theorems for the algebraic $\mathrm{K}$-theory of stable $\infty$-categories.
It is based on a general formula for the evaluation of an additive functor on a
Verdier quotient closely following work of Waldhausen. We also include a new
proof of the additivity theorem of $\mathrm{K}$-theory, strongly inspired by
Ranicki's algebraic Thom construction, a short proof of the universality
theorem of Blumberg, Gepner and Tabuada, and demonstrate that the cofinality
theorem can be derived from the universal property alone.
