Abstract of Thesis (Ph. D.)--University of Michigan, 1912. / Cover title. "Reprinted from the Physical review, n.s., vol. 111, no. 4, April, 1914."

Thesis (Ph. D.)--Princeton University, 1932.

Thesis (M. Phil.)--University of Hong Kong, 1992.

Proefschrift--Leyden. / "Samenvatting": p.[164]-169. Includes bibliographical references.

Abstract of thesis (Ph. D.) -- University of Michigan, 1912. / Cover title. "Reprinted from the Physical review, n.s., vol. 111, no. 4, April, 1914."

Thesis (Ph. D.)--Princeton University, 1931.

Proefschrift--Leyden. / "Samenvatting": p.[164]-169. Includes bibliographical references.

Thesis (Ph.D.)--Montana State University--Bozeman, 2007. / Typescript. Chairperson, Graduate Committee: Joseph A. Shaw. Includes bibliographical references (leaves 191-198).

Thesis (M.S.)--University of Delaware, 2009. / Principal faculty advisor: Sandeep Patel, Dept. of Chemistry & Biochemistry. Includes bibliographical references.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science. Johannesburg, 24 May 2014. / The Sunyaev-Zel'dovich e ect (hereafter SZE), i.e. the distortion of the cosmic microwave background (CMB) spectrum due to inverse Compton scattering of CMB photons o energetic electrons in cosmic structures, is a relevant inves- tigation tool for astrophysical and cosmological studies. Since the SZE is an interaction between photons and electrons, polarization arises as a natural out- come and then provides the SZE with an important complementary component as an astrophysical and cosmological probe. This thesis is an extensive study on the SZE in non-relativistic and relativistic regime including polarization. We rst perform a study on a set of galaxy clusters hosting radio halos where we constrain the non-thermal pressure present in these structures using multifre- quency data such as SZE, radio and X-ray. We found that the average ratio between non-thermal to thermal pressure is 0:5. We then derive, in the full relativistic regime, a general formulation of the properties of the SZE, and we further derive the Stokes parameters, Q and U, of the polarized SZE. This is done in a general case by solving the polarized Boltzmann collisional integral in the Thomson limit that allows us to extract the Stokes parameters for arbitrary electron distribution functions. We further discuss the spectral features of the SZE polarization as produced by other additional e ects occurring in the clus- ter atmospheres, like nite optical depth e ects and transverse plasma motions. We nally apply the results of our study to di erent cosmic structures (e.g. galaxy clusters and radio galaxies) and we discuss the relevance of SZE polar- ization in the study of extragalactic astrophysical plasmas and for cosmological applications.