Abstract: In deformation quantisation, one passes from a classical system to a quantum system by deforming the commutative algebra of classical observables into a noncommutative algebra of quantum observables in a manner consistent with the correspondence principle. In the presence of a smooth action of a compact abelian Lie group $G$ (e.g., a torus), one can rigorously effect deformation quantisation through a method, due to Rieffel, called strict deformation quantisation. In this talk, I'll give an introduction to strict deformation quantisation of Frechet $G$-pre-$C^\ast$-algebras, together with the corresponding deformation of $G$-equivariant finitely generated projective modules and $\ast$-representations. If time permits, I'll also introduce Connes--Landi deformation, which, as was observed by Sitarz and Varilly, is precisely strict deformation quantisation for $G$-equivariant spectral triples.