The potential vorticity (PV) theory is based on the analysis methods of isentropic PV. This paper aimed at the introduction to the basic concepts and methods which are necessary to grasp to do the analysis of isentropic PV. It first gave the fundamentals of potential temperature and PV, troposphere and stratosphere, front and tropopause, and then discussed the characteristics of front and tropopause in the vertical cross sections, isobaric surface maps, and isentropic surface maps. Different kinds of chart instances were illustrated in this paper. Through analyses and comparisons, the results are obtained as follows. The high PV in stratosphere originates from the large vertical gradient of potential temperature which increases sharply with height above the tropopause. The vertical gradient of potential temperature is the main factor which determines PV distribution. The isentropic PV maps mainly reflect the activity of polar air mass, and the front, jet, and tropopause closely associated with polar air mass. In the end, this paper pointed out that some wrong knowledges should be avoided in the isentropic PV analyses, especially, we should avoid treating streamlines in the isentropic surface as trajectories and cannot obtain such a wrong deduction that the stratospheric dry air can intrude into the lower troposphere.