This books presents one and two dimensional analytical solutions for solute transport in homogeneous porous formations. The constant and time dependent forms of input concentration are considered to predict the contaminant concentration distribution along or against unsteady groundwater flow in semi-infinite and finite aquifers. An exponentially decreasing unsteady velocity distribution is considered. The sinusoidal form of time dependent velocity distribution is also considered which represents seasonal variation in year in tropical regions. The direct relationship between dispersion coefficient and seepage velocity concept is used in which dispersion coefficient is directly proportional to the seepage velocity. When the groundwater table rises and falls, the velocity of flow in the aquifer may be transient or unsteady which is considered here. The Laplace Transform Technique (LTT) and the Hankel Transform Technique (HTT) are used to derive analytical solutions which would be useful to benchmark numerical codes and solutions.