The objective of this thesis is to study the fluid oscillation modes in compact stars, understand their properties and infer stellar structures from their frequencies. The first part of the thesis focuses on the Newtonian theory of stellar pulsation and the Cowling approximation (CA), which neglects the change in gravitational potential. We modify the conventional CA, devise a more accurate version of the CA and calculate the first-order correction to the conventional CA. In the second part, we apply the variational approximation method proposed by Chandrasekhar [Astrophys. J. 139,664 (1963)] and δ-perturbation expansion proposed by Bender et. al. [J. Maths. Phys. 30, 1447 (1989)] to explain the universality in the relationships between the fundamental mode frequency and the moment of inertia of neutron stars, which was discovered by Lau et. al. [Astrophys. J. 714, 1234 (2010)]. We reveal that stiff equations of state are the conditions for the observed universality. In the third part, we consider the relativistic pulsation formulation and relativistic CAs for compact stars. We unify several known CAs with a single second-order differential equation. We also extend the modified CA derived from the formalism established by Allen et. al. [Phys. Rev. D 58, 124012 (1998)] to include the effect of buoyancy. Finally, we find the first-order and the second-order post-Newtonian expansions for the nonradial pulsations in quark stars. We derive an analytic formula expressing the fundamental mode frequency in terms of the compactness of quark stars. As a result, we are able to verify the universality mentioned above for quark stars. / 這論文是對在牛頓力學以及相對論框架下緻密星流體振盪的研究結果。論文第一部分集中討論牛頓力學下流體振盪以及近似方法。這近似方法忽略重力勢的擾動，令系統由四階微分方程減少為二階微分方程。我們修正了已往的近似方法和提出一個更精準的近似方法。第二部分包括變分近似方法。我們利用該方法和δ微擾理論解釋基本模式頻率的普通性。第三部分包括相對論框架下緻密星流體振盪和近似方法。我們以一條二階微分方程總結之前出現的近似方法並且在近似方法中加入浮力。最後，我們執行一階和二階的後牛頓展開，以分析夸克星的基本模式。我們驗證了展開的準確度和發現了基本模式頻率的方程。 / Chan, Tsang Keung = 有關在緻密星中流體振盪的研究 / 陳增強. / Thesis M.Phil. Chinese University of Hong Kong 2013. / Abstracts also in Chinese. / Title from PDF title page (viewed on 07, October, 2016). / Chan, Tsang Keung = You guan zai zhi mi xing zhong liu ti zhen dang de yan jiu / Chen Zengqiang. / Detailed summary in vernacular field only.