Let $\mathrm{X}$ be a topological space of holomorphic functions on the open unit disc $D$. The study of the geometry of a space $X$ is centered on the identification of the linear isometries on $\mathrm{X}$, and there is an obvious connection between weighted composition operators and isometries. This connection can be traced back to Banach himself and emphasized by Forelli, El-Gebeily, Wolfe, Kolaski, Cima, Wogen, Colonna and many others. A characterisation is given of all the linear isometries of Hol($\Omega$), the Fr´ echet space of all holomorphic functions on $\Omega$ when $\Omega$ is the unit disc or an annulus, endowed with one of the standard metrics. Further, the larger class of operators isometric when restricted to one of the defining seminorms is identified. This is a joint work with Lucas Oger and Jonathan Partington.[-]