The topological aspects of superconductivity on doped Weyl semimetals are investigated. / Topological phases of matter have sparked significant experimental and theoretical interest due to the topologically robust edge modes they host, as well as their classification through rich mathematics. An interesting example of a topological phase in three dimensions, the Weyl semimetal, can exhibit topological ordering through the existence of Fermi arcs on the surfaces of the material. For the doped Weyl semimetal, we investigate possible resulting Weyl superconducting states --- both the inter-Fermi surface pairing state following Li and Haldane, and the intra-Fermi surface pairing state following Burkov --- in this thesis, and study their topological properties by computing the gapless Weyl-Majorana edge modes they host. The results obtained in Ref. \cite{LH} for the inter-Fermi surface superconducting state are reproduced, and the bulk and edge properties of the intra-Fermi surface pairing superconducting state are studied in detail. / Thesis / Master of Science (MSc) / In this thesis, we study an interesting class of topological materials called the Weyl semimetal as well as its associated superconducting phases. A description of the Fermi arcs on Weyl semimetals are given, and the topological properties of the inter-Fermi surface and intra-Fermi surface pairing states are studied in detail.