The authors make an interesting study of the n-dimensional Laplace transform defined by \[ F(s;t)=L[f(t);s]=\int^{\infty}_{0}\int^{\infty}_{0}...\int^{\inf ty}_{0}\exp [-(s.t)]f(t)p_ n(dt), \] where \(t=(t_ 1,t_ 2,...,t_ n)\) and \(s=(s_ 1,s_ 2,...,s_ n)\) with \(s.t=\sum^{n}_{r=1}s_ rt_ r\) and \(p_ n(dt)=\prod^{n}_{k=1}dt_ k\). The inverse transform is given by \[ L^{-1}[F(s);t]=\frac{1}{(2\pi i)^ n}\int^{c_ 1+i\infty}_{c_ 1-i\infty}\int^{c_ 2+i\infty}_{c_ 2-i\infty}...\int^{c_ n+i\infty}_{c_ n- i\infty}\exp [s.t]F(s)p_ n(ds). \] They develop a useful method of computing Laplace transform pairs of n-dimensions from known one- dimensional Laplace transforms. Several new theorems for calculating Laplace transform pairs of n-dimensions are proved with examples. Their method is then applied to solve one-dimensional and two-dimensional boundary value problems. This work would help to solve other boundary value problems of physical and engineering interest.