The terahertz time-domain spectroscopy (TDS) technique which combines broadband and highly sensitive coherent detection with time revolution and strong immunity to background has found application in a wide range of fundamental disciplines. This work presents the development of a polarisation resolved THz-TDS spectrometer that enables sensitive studies of the optical activity of chiral metamaterials in the terahertz frequency range. The thesis is divided into two principal parts. The first (chapters 2 to 4) describes the principles of the time-domain spectroscopy. This is followed by descriptions of a crossed-bowtie antenna which simultaneously detects both orthogonal field components and devices for measuring the state of polarisation of THz waves. In particular we present experimental and computational studies of four linear polarisers. One is a pile-of-plates which relies on the different reflectivity of s and p-polarised light incident on a dielectric surface at Brewster’s angle and the others are wire-grids of different dimensions and different substrates which rely on the anisotropic conductivity of thin metal wires. The design of the polarisation resolved spectrometer and a formalism for describing optical activity and analysis data are then described in the fourth chapter. The second part of the thesis describes applications of the polarisation sensitive terahertz TDS system to the study of optical activity exhibited by artificial materials. Four structures have been studied in this work; metal screw hole arrays, quasi-two-dimensional gammadions and Archimedean spiral metamaterials and a quasi-three-dimensional array of spirals. Experimental and computational studies of the polarisation characteristics and the optical properties of these structures are discussed in chapters 5, 6 and 7.