The aim of this thesis is to give a rigorous analysis of the Einstein field equations which arise when modelling the collapse of a scalar field in self-similar, whole-cylinder symmetry. The principal motivation is to discover whether, and under what conditions, this class of spacetimes admit the existence of a naked singularity. Imposing self-similarity on the spacetime gives rise to a set of single variable functions describing the metric. Furthermore, it is shown that the scalar field is dependent on a single unknown function of the same variable and that the scalar field potential has exponential form. The Einstein equations then take the form of a set of ODEs, with two degrees of freedom and a free initial datum, where initial data is given on the regular axis. Self-similarity also gives rise to a scalar curvature singularity at the scaling origin, to the future of the regular axis. The field equations have singular points along the axis and along the past and future null cones of the singularity, labelled N− and N+, respectively. We label the region between the axis and N− as region I and the region bounded by N− and N+ as region II. The problem naturally divides into two stages, that is, solving the equations in these two separate regions. The independent variable may be rescaled in each separate region to obtain an autonomous system of field equations and a dynamical systems approach is used to obtain qualitative solutions. It is shown that some solutions have a maximal interval of existence ending either on or before N−, where the termination of the solution corresponds to either a spacetime singularity or future null infinity, and that some solutions may be extended into region II. A ll of these solutions are then shown to terminate in a spacelike singularity before reaching N+. This supports the Cosmic Censorship Hypothesis.