Practical Meteorology: An Algebra-based Survey of Atmospheric Science
by Roland Stull · University of British Columbia
Free 22-chapter university textbook from UBC. It covers radiation, thermodynamics, stability, clouds, radar and satellites, weather-map analysis, fronts, cyclones, thunderstorms, hurricanes and numerical weather prediction, with worked examples and exercises that need only algebra. This is the strongest free full-course text for the topic. It goes from first principles through map analysis, fronts, storms and NWP. It is far more rigorous than intro sites but needs no calculus.
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