This thesis presents a study of the kinematics, physical conditions and chemical abundances for a sample of Galactic planetary nebulae (PNe) with Wolf-Rayet (WR) and weak emission-line stars (wels), based on optical integral field unit (IFU) spectroscopy obtained with the Wide Field Spectrograph (WiFeS) on the Australian National University 2.3 telescope at Siding Spring Observatory, and complemented by spectra from the literature. PNe surrounding WRtype stars constitute a particular study class for this study. A considerable fraction of currently well-identified central stars of PNe exhibit 'hydrogen-deficient' fast expanding atmospheres characterized by a large mass-loss rate. Most of them were classified as the carbon-sequence and a few of them as the nitrogensequence of the WR-type stars. What are less clear are the physical mechanisms and evolutionary paths that remove the hydrogen-rich outer layer from these degenerate cores, and transform it into a fast stellar wind. The aim of this thesis is to determine kinematic structure, density distribution, thermal structure and elemental abundances for a sample of PNe with different hydrogen-deficient central stars, which might provide clues about the origin and formation of their hydrogen-deficient stellar atmospheres. Hα and [N II] emission features have been used to determine kinematic structures. Based on spatially resolved observations of these emission lines, combined with archival Hubble Space Telescope imaging for compact PNe, morphological structures of these PNe have been determined. Comparing the velocity maps from the IFU spectrograph with those provided by morpho-kinematic models allowed disentangling of the different morphological components of most PNe, apart from the compact objects. The results indicate that these PNe have axisymmetric morphologies, either bipolar or elliptical. In many cases, the associated kinematic maps for PNe around hot WR-type stars also show the iii Copyright Statement Under Section 35 of the Australian Copyright Act of 1968, the author of this thesis is the owner of any copyright subsisting in the work, even though it is unpublished. Under Section 31(I)(a)(i), copyright includes the exclusive right to 'reproduce the work in a material form'. Thus, copyright is infringed by a person who, not being the owner of the copyright, reproduces or authorizes the reproduction of the work, or of more than a reasonable part of the work, in a material form, unless the reproduction is a 'fair dealing' with the work 'for the purpose of research or study' as further defined in Sections 40 and 41 of the Act.This thesis may therefore be copied or used only under the normal conditions of scholarly fair dealing for the purposes of research, criticism or review, as outlined in the provisions of the Copyright Act 1968. No part of this thesis or the information therein may be included in a publication or referred to in a publication without the written permission of the author. Proper written acknowledgement should be made for any assistance made ...