This thesis describes a method for calculating the short-circuit voltage of a transformer using conformal mappings. The space inside the core window and the space outside the core in longitudinal and transverse cross-sections are mapped to a unit disk where magnetic flux density is calculated. The short-circuit voltage is calculated by the integration of the energy of the leakage field in the windings and the space around the windings, excluding the core. This method takes into account windings of different heights, the fringing effect at the ends of the windings and any relative position of windings located on the same or different limbs. The method has been tested on three-phase distribution transformers, power transformers and special single-phase transformers. The original scientific contributions of this thesis are the following: 1) method for calculation of transformer leakage field and short-circuit voltage using conformal mappings in longitudinal and transverse cross-sections of core and transformer windings, 2) numerical procedure for calculating the energy of the transformer leakage field in three-dimensional space by extrapolation of two-dimensional field solutions in longitudinal and transverse cross-sections obtained by using conformal mappings and 3) an algorithm for calculating the current distribution through parallel-connected sections of a transformer high-voltage winding with an asymmetric arrangement of short-circuited low-voltage windings in a transformer window and an asymmetric magnetic field distribution in short-circuit tests.