Elementary Lecture Note or Book on Modular Form for Beginner or Amateur or Self Study or Self Learning

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I have searched and found a pdf file of Don Zagier, but having trouble to understand periodicity with Fourier function/transformation, Rieman Surface, lattice.

Can any one suggest me lecture notes or a book where things are explained more elaborately? This post didn't help.

My purpose is to understand Modular Form in regard with number theory.