Radiation fog forms when a moist airmass near the surface of the earth is cooled by losing heat to a calm, clear sky. This is the type of fog that we get here in South Florida on occasion. Advection fog usually forms when a warm airmass moves over cooler water, the moisture in the air condenses, fog forms and is transported by the wind from one place to another. This usually occurs in places like London and San Francisco.
Barometric pressure is a measure of how hard the air is pushing.
At sea level, there is more air pressing on us than up on top of a mountain so the barometer is higher. When a storm approaches, the barometer often goes down. As the skies clear, the atmospheric pressure rises again. The study of meteorology is rooted in physics and math with a sprinkle of chemistry, geology and basic Earth science. There are many good schools that offer four year degree programs including UM, FSU, Penn State, Ohio State and Purdue.