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One of the most promising routes to create advanced materials is self-assembly. Self-assembly refers to the self-organisation of building blocks to form ordered structures. As the properties of the self-assembled materials will inherit the properties of the basic building blocks, it is then possible to engineer the properties of the materials by tailoring the properties of the building blocks. In order to create mesoscale materials, the self-assembly of molecular building blocks of different sizes and interactions is important. Mesoscopic materials can be obtained by using larger building blocks such as nano and colloidal particles. Colloidal particles are particularly attractive as building blocks because it is possible to design interparticle interactions by controlling both the chemistry of the particles' surface and the properties of the solvent in which the particles are immersed. The self-assembly of spherical colloidal particles has been widely reported in the literature. However, advances in experimental techniques to produce particles with different shapes and sizes have opened new opportunities to create more complex structures that cannot be formed using spherical particles. Indeed, the particles' shape and effective interactions between them dictate the spatial arrangement and micro-structure of the system, which can be engineered to produce functional materials for a wide range of applications. The driving forces determining the self-assembly of colloidal particles can be modified by the use of external influences such as geometrical confinement and electromagnetic forces. Geometrical confinement, for example, has been used to design quasi two-dimensional materials such as multi-layered structures of spheres, dimers, rods, spherical caps, and monolayers of platelets with various geometries and symmetries. In this dissertation, we present three computer simulations studies using Monte Carlo and Molecular Dynamics simulations determining the self-assembly of monolayer colloidal platelets with different shapes confined in two dimensions. These particles have been selected due to recent experiments in colloidal particles with similar shapes. All the particles' models are represented by planar polygons, and three different effects affecting their self-assembly have been analysed: (a) the curvature of the particles' vertices; (b) the curvature of the particles' edges; and finally (c) the addition of functional groups on the particles' surface. These studies aim to demonstrate that the subtle changes on the particle's shape can be used to engineer complex patterns for the fabrication of advanced materials. Monte Carlo simulations are performed to study the self-assembly of colloidal platelets with rounded corners with 4, 5, and 6-fold symmetries. Square platelets provide a rich phase behaviour that ranges between disorder-order and order-order phase transitions. Suprisingly, the disk-like shape of pentagons and hexagons prevents the total crystallisation of these systems, even at a high pressure state. A hysteresis gap is observed by the analysis of compression and expansion runs for the case of square platelets and the thermodynamic method known as direct coexistence method is used to be accurately determined the point of the order-order transition. Further, unexpected results are obtained by performing Molecular Dynamics simulations in systems with platelets with 3, 4, 5, and 6-fold symmetries when all the sides of each polygon are curved. Macroscopic chiral symmetry breaking is observed for platelets with 4 and 6-fold symmetries, and for the first time a rule is promoted to explain when these chiral structures can be formed driven only by packing effects. This unique rule is verified also for platelets with the same curved sides as previously when functional chains tethered to either vertices or sides. Indeed, square platelets with curved sides confined in two dimensions can form chiral structures at medium densities when flexible chains tethered to either vertices or sides. Triangular platelets with curved sides can form chiral structures only when the chains are tethered to the corners, since the chains experience an one-hand rotation to sterically protect one side. When the chains are symmetrically tethered to the sides, local chiral symmetry breaking is observed as both left-hand and right-hand sides on each vertex are sterically protected allowing the same probability for rotation either in clockwise or anticlockwise direction.

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