This volume contains forty of the papers presented at the International Conference on 'Mathematics in Transport Planning and Control' which was held at Cardiff University from 1-3 April, 1998. This was the third such conference run under the auspices of the Institute of Mathematics and Its Applications, the first being held at the University of Surrey in 1979, and the second at Cardiff University in 1989. Over fifty papers were submitted for presentation at the conference. It will be clear from the contents that mathematical ideas and methodologies continue to play a prominent part in the description and solution of the many and varied problems that are being currently investigated in quite diverse areas of transport research. Applications will be found on transport planning, congestion, assignment, networks, signalling, road safety, and environmental issues.