I get this question a lot. So here is a list of books that give comprehensive introduction to the vast science of Vedic Astrology or Jyotish.
I recommend to pick one of these three and start there. As you grasp the basic of Vedic Astrology, you can dive deeper into more complex topics of chart reading such as nakshatras, vargas, panchanga, and many others.
List of Books to learn basics of Vedic Astrology
Light on Life by Hard de Fouw & Robert Svoboda
Astrology of the Seers by David Frawley
Science of Light, An Introduction to Vedic Astrology by Freedom Tobias Cole
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