HTS magnets have been developed to generate high magnetic fields because its high critical field at low temperatures. For HTS magnets, the design of thermal stability and protection is based on understanding of its quench behaviour. However, there are few experimental and numerical results on the quench behaviour of HTS at low temperatures. This thesis work is mainly dedicated to investigate the quench behaviour of high temperature superconductor (HTS) at low temperatures by 1D and 2D numerical analysis. In addition, this work also investigates the critical current of HTS coils made from Bi/Ag2223 tape at 77K under self-field. The ANSYS implementation of a general quench model capable of handling nonlinear heat generation over a large temperature range of current sharing, e.g. for HTS at low temperatures, has been successfully validated for HTS at high temperatures and LTS with reference to predictions by the classical quench theory. The numerical model also revealed that the classical theory usually overestimates the minimum quench energy MQE as self-heating is neglected during the development of MPZ. The effective medium approximation for the coil thermal-electrical properties was also found to be sufficient for practical HTS coils. Simulation of 1D HTS conductors at low temperatures using the non-linear heat generation model revealed a different quench behaviour from that of LTS conductors. Firstly, while the minimum quench energy MQE is well defined, it is almost an order of magnitude smaller than the enthalpy of the minimum propagation zone. Hence the growth of MPZ is entirely due to self-heating while MQE is just a sufficient trigger. Secondly, for a practically defined MQE with 95% of the ”true” minimum, there is a large variation of the size of MPZ and the corresponding quench temperature. Thirdly, there appears a simple scaling between the average MPZ heat generation Gq and the temperature range (Tq − Tcs) of MPZ. 2D analysis of HTS coils showed the MQE is an order of magnitude larger than that from 1D analysis because of radial heat conduction. For practical coils, the geometry ii and boundary cooling have an important influence on their quench behaviour while the MPZs are larger and hotter. Two single pancake coils of 50mm inner diameter and 20 turns were manufactured and tested at 77K. The current carrying characteristics of HTS coils was evaluated by using the method based on the Ic-B of bifilar tape and agree well with measured results. One bifilar pancake coil was fabricated and tested at 77K. The measured critical current is 108A and about 20% larger than that of a single pancake coil.