This volume contains 25 of the 60 papers presented at The second international conference on 'Computational Methods and Function Theory', also called CMFT'94, which took place at the Universiti Sains Malaysia, Penang, Malaysia, during March 21-25, 1994. Its aim was to stimulate fruitful interactions between computational methods, or scientific computation and pure and applied complex analysis which relies heavily on the power of computers and their sophisticated software, both of which have substantially contributed to the recent progress in mathematics and the applied sciences. Topics covered encompass all areas of the general theme of this conference. In addition to several important selected topics of complex analysis, this volume also contains state-of-the-art research articles on potential theory as well as the theory of approximations.