LaplaceTransform[expr, t, s] gives the Laplace transform of expr.
LaplaceTransform[expr, , , ... , , , ... ] gives the multidimensional Laplace transform of expr.
The Laplace transform of a function is defined to be .
The lower limit of the integral is effectively taken to be , so that the Laplace transform of the Dirac delta function is equal to 1.
Assumptions and other options to Integrate can also be given in LaplaceTransform.
In TraditionalForm, LaplaceTransform is output using .
See The Mathematica Book: Section 1.5.11 and Section 3.5.11.
See also: InverseLaplaceTransform, FourierTransform, ZTransform, Integrate.