Scuba diving is all about making sure you get enough air in you while underwater.  Simple enough? Its actually complicated because of how air acts under different pressures, depths and in your body and equipment.  In order to obtain your scuba certification it is important to know and understand the physics behind the operation; mainly a few associated Gas Laws.

Boyles Law relates the pressure and volume of a gas that is held at constant temperature.

                            P₁V₁=P₂V_{2
 Where P=pressure, V=volume and the subscripts 1 and 2 represent the initial and final states.  Essentially what Boyles law is saying is that pressure and volume are inversely related. 
If you increase the pressure then the volume will decrease; and if you increase the volume then the pressure will decrease.}

_{Charles Law relates temperature and volume at a constant pressure.}
                            T₁/V₁=T₂/V₂
Where T=temperature, V=volume and the subscripts 1 and 2 represent the initial and final states.  Charles Law states that a decrease in temperature will decrease its volume which also implies that if the volume were to remain constant there would have to be an increase in pressure.  Imagine it is a beautifully sunny day and you are at the beach, your scuba gear is packed in your trunk, including your tank and you are just basking in the sun for a bit (clearly not located in Fairbanks Alaska).  However when you return to your car, your scuba tank has exploded! Charles law explains why that happened.  Your tank stayed at a constant volume but had an increase in temperature due to the hot sun, therefore the pressure increased and provided perfect conditions for an explosion. 

Henry's Law:
                            P=KC
Where P=pressure, C is the concentration of the gas and K is Henry's law constant.  This law tells the diver that at higher pressures our bodies will absorb more gasses.  The deeper the dive, the greater the amount of nitrogen absorbed into the body.  Therfore the greater the depth the greater the risk of decompression illness.

Dalton's Law of Partial Pressure simply states that the pressure exerted by a mixture of gases is equal to the sum of the pressures that would be exerted by the gases individually.
                            P=p1+p2+p3+...pN
Where P is total pressure due to the partial pressures p. This tells us that all gases tend to compress equally by volume.

                   Boyles Law                                               Charles Law                                                            Henrys Law                                                Daltons Law