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In this thesis, we present the basic concepts of isogeometric analysis (IGA) and we consider Poisson's equation as model problem. Since in IGA the physical domain is parametrized via a geometry function that goes from a parameter domain, e.g. the unit square or unit cube, to the physical one, we present a class of parametrizations that can be viewed as a generalization of polar coordinates, known as the scaled boundary parametrizations (SB-parametrizations). These are easy to construct and are particularly attractive when only the boundary of a domain is available. We then present an IGA approach based on these parametrizations, that we call scaled boundary isogeometric analysis (SB-IGA). The SB-IGA derives the weak form of partial differential equations in a different way from the standard IGA. For the discretization projection
on a finite-dimensional space, we choose in both cases Galerkin's method. Thanks to this technique, we state an equivalence theorem for linear elliptic boundary value problems between the standard IGA, when it makes use of an SB-parametrization,
and the SB-IGA. We solve Poisson's equation with Dirichlet boundary conditions on different geometries and with different SB-parametrizations.