Brigham's book on the Fast Fourier Transform was an eye opener for me. Not so much because of the "Fast" part (which is super interesting and useful too) but it

Brigham's book on the Fast Fourier Transform was an eye opener for me. Not so much because of the "Fast" part (which is super interesting and useful too) but it was the introduction I needed to make integral transforms and convolution click. And that helped tremendously to connect a whole bunch of other dots.