Aspects of Snyder geometry

The Snyder spacetime represents the first proposal of noncommutative geometry. It still retains a significant role because of its property of preserving Lorentz invariance. In the thesis, several different aspects of the model are investigated. In particular, the results include: a calculation of the orbits of a particle in Schwarzschild spacetime in the setting of the relativistic Snyder geometry; the definition of the path integral in one- and two-dimensional Snyder space, in the traditional setting and using the Faddeev-Jackiw formalism; a study of the representations of the three-dimensional Euclidean Snyder-de Sitter algebra (namely, the extension of the Snyder model to a spacetime background of constant curvature) with the calculation of the spectrum of the operators of position and momentum squared; a generalisation of the Snyder model, which includes all possible deformations compatible with Lorentz invariance, and an investigation of it within the Hopf algebroid setting, including the discussion of the twist operator, the R-matrix and the deformed addition of momenta.