Chapter 1 gives a brief review of the relevant aspects of stellar evolution leading to the formation of a planetary nebula. Included in this review is a discussion of the most important factors which appear to dictate the shaping and general characteristics of these nebulae. Chapter 2 follows with a review of polarization theory and its use in the study of planetary nebulae and the interstellar medium. This includes a description of the basic reduction procedures which are used to produce the polarization maps of later chapters. Discussion of the reduction process is accompanied by the analysis and interpretation of linear polarization data from the observation of an extragalactic source. Chapter 3 presents multicolour polarimetry data for the young bipolar planetary nebula M2-9. Much of the polarization data confirms previously gathered results and shows that extreme levels of polarization occur in the outer regions of the nebula. Polarization structure within the central regions of M2-9, however, appear to contradict a number of previously gathered results and suggest that the central illuminating source of the nebula is extended. The data conclusively proves that the mirror-symmetric condensations have changed position. An estimation of the rotation period of the condensations has been made using calculations which trace their lateral displacement. The result of these calculations agrees well with previously gathered results. Chapters 4 and 5 present new multicolour polarimetry data for the evolved bipolar planetary nebulae NGC 2440 and NGC 2818. Results provide evidence for the existence of bipolar rotating episodic jets in the evolved Type I bipolar nebulae. The data also shows that both nebulae possess low polarization levels and a lack of clear structure within the polarization pattern. Consequently, the dust distribution of planetary nebulae must become less favourable for the production of radiation scattering with age
