Description: This paper proposes a more generalized Gerber-Shiu G-S function which contains both the G_S expected discounted penalty function and dividends paid up to ruin, as well as many others that have not been taken into consideration in the same systematic way, such as the insurer's accumulative utility, expected total discounted claim expenses, etc. The major result provides a unifying approach for all ruin-related quantities that fall in the category of the generalized GS function. From the Actuarial Research Clearing House, 2008, Vol. 1.