Why does it create higher pressure at the higher altitude though. Afterall, the atmosphere is not enclosed so it isn't like heating the gas inside a closed box.
The mental model that I use, rather like BOAC's, is that of a column of air with pressure levels marked as stripes. If the air is warmer than the surrounding air, the column will stretch like a concertina, and the vertical separation between the stripes will be greater than in the surrounding air. Thus if the pressure levels are aligned at the surface, the warmer air will have higher pressure than its surroundings at the top. In reality, things will equilibrate a little, and there will tend to be lower pressure at the surface, and higher pressure at the top.
If you don't like the model of the atmosphere expanding in vertical columns, that's fair enough, but what
is determined by the laws of physics is the separation between pressure levels as a function of the temperature of the air.
For books, I'd recommend
Bradbury and possibly
Stull.