Power transformers are important and expensive elements within the electric power transmission and distribution utilities. Since these equipments are connected in series to the network, any inadvertent failures would cause catastrophic interruptions to the power supply. As such, it is extremely critical for the power transformer to operate continuously in order to maintain a reliable and efficient electricity supply. Ageing or defects in power transformer has a root in its insulation structure and this has always been a well-known fact. For many years, mineral oil impregnated cellulose paper (OIP) has been the choice of insulation for power transformers due to its excellent dielectric properties as well as its inexpensive price. During the course of operation, the dielectric properties of OIP insulation inevitably deteriorate due to singularly or a combination of stresses such as thermal, electrical, mechanical, chemical as well as environmental stresses. Degradation of power transformer insulation is an irreversible process and has been encountered by all power utilities around the world. However, replacing a power transformer simply by its age is impractical and uneconomical. With the increase in the population of ageing power transformers, there is an urgent need to evaluate the condition of transformer insulation so as to facilitate the planning for refurbishment or replacement of the equipment in a more appropriate manner. To address this issue, many techniques involving both chemical and electrical methods have been developed to monitor the insulation condition of oil-filled power transformers. However, some of these techniques are destructive by nature and some of them are unable to assess the insulation condition accurately. With the advancement in technology over the years, newer diagnostic methods in time and frequency domains have been developed in recent years to assess the insulation condition based on their dielectric responses. One of the newly developed methods is known as Frequency Domain Spectroscopy (FDS) measurement and it monitors the insulation condition by measuring the diagnostic parameters as a function of frequency ranging from 0.1mHz to 1kHz. The primary focus of this thesis is to adopt FDS technique to study the effects of several deterioration factors on the dielectric response of transformer insulation, so as to develop a better understanding between FDS technique and the condition of transformer insulation. To study the effects of moisture and temperature, FDS measurements were performed on a CIGRE model transformer at various moisture concentrations and temperature levels. From the experimental results, moisture and temperature have significant impacts on the dielectric response of transformer insulation. In addition to constant temperature, FDS measurements were also performed during transient temperature conditions to investigate the effects of transient temperature on the dielectric response of transformer insulation. An empirical relationship between the dielectric response produced from transient and steady temperature conditions was able to be established from the experimental results. A novel approach to study the effects of geometrical parameters was also part of this research work. An insulation model has been designed and fabricated for the purpose of this study. FDS measurements were conducted on the insulation model with different configurations of barriers, spacers and oil volume. The results showed that geometrical parameters did have an impact on the dielectric response of transformer insulation. The secondary diagnostic technique used in this research is Polarisation and Depolarisation Current (PDC) measurement and the purpose of using this method is to explore the feasibility of reducing the total PDC measurement duration as well as to determine the optimum measurement time for PDC.