The ISAAC Group in Pseudo-Differential Operators (IGPDO) met at the Fifth ISAAC Congress held at Università di Catania in Italy in July, 2005. This volume consists of papers based on lectures given at the special session on pseudodifferential operators and invited papers that bear on the themes of IGPDO. Nineteen peer-reviewed papers represent modern trends in pseudo-differential operators. Topics include partial differential equations, global analysis, geometry, quantization, Wigner transforms, Weyl transforms on Lie groups, mathematical physics and timefrequency analysis. The articles will be of interest to graduate students and researchers in analysis, mathematical physics and mathematical sciences. This collection of essays and research articles under the banner of IGPDO is a valuable complement to the volumes ''''Advances in Pseudo-Differential Operators'''' and ''''Pseudo-Differential Operators and Related Topics'''' published in the same series in 2004 and 2006, respectively.