Earth-borne contaminants can include toxic and hazardous materials that can be introduced into the geo-environment as a result of the use of pesticides, emissions and leakage from waste storage lagoons derived from mineral processing, hazardous materials storage sites and other human activities that involve events such as gasoline spills and leaks. When such materials enter the earth environment their migration involves complex process governed by the nature of the contaminant, the nature of the geological material and the presence of ground water. The three dominant processes that lead to the contaminant movement include the advective transport by virtue of ground water flow, diffusive transport as a result of decay of the concentration and attenuation resulting from the entrapment of the contaminant in the geological medium. The advective transport process is the most dominant that is governed by the flow characteristics of the ground water. This process dictates the strength and rate at which the contaminant can migrate within the geomaterial. This lecture will illustrate the mathematical principles underlying the advective transport process and illustrate simple mathematical solutions that can be used to enhance the decision making process in the absence of firm data on the physical properties governing the transport process.