Khaled Muhammad Al-Furati2022-05-182022-05-185482https://drepo.sdl.edu.sa/handle/20.500.14154/2343This thesis is about Watson's Lemma. This lemma describes the behavior of the Laplace and Laplace-Stieltjes integrals near infinity. Consequently, we can use this lemma to find asymptotic expansions of functions that can be written in the Laplace or Laplace-Stieltjes integral form. This study is mainly based on the Riemann-Stieltjes and Laplace-Stieltjes integrals.enThesis