Seismology is how we see inside a planet we can never cut open: by reading the waves that earthquakes send through it. It spans the dramatic surface story of quakes and faults and the deep quantitative theory of elastic waves, and the reading order should move between them so the mathematics always has physical meaning attached.
The path below starts with the accessible earthquake science, builds the geological and wave-theoretic foundations, and finishes with the quantitative and data-driven methods professionals actually use. It suits earth-science students and serious enthusiasts alike.
The accessible entry
Start with Earthquakes, Bruce Bolt's classic, readable introduction to why the ground shakes, how faults rupture, and how we measure it. Pair it with The earth, Tarbuck's broad physical-geology text that situates seismology within plate tectonics and the planet's structure. Together they give you the big picture before the equations arrive.
Foundations and wave theory
Now build the core. An Introduction to Seismology, Earthquakes, and Earth Structure by Stein and Wysession is the standard modern textbook, connecting earthquake source, wave propagation, and Earth structure in one coherent framework. Introduction to seismology by Shearer is the other widely used graduate text, especially strong on the theory of seismic waves. Reading both gives you the elastic-wave foundation from two well-regarded perspectives.
The quantitative core and frontier
The deep end is unavoidable for real work. The mechanics of earthquakes and faulting by Scholz is the definitive treatment of the physics of faults, friction, and rupture. Quantitative seismology by Aki and Richards is the field's great reference, rigorous and comprehensive on wave theory and source mechanics. Seismic Data Analysis by Yilmaz is the practical bible for processing reflection data, essential on the exploration side, and Seismological Grand Challenges in Understanding Earth's Dynamic Systems closes the path by surveying the open problems that define where seismology is heading.
Read in this order, seismology turns from a collection of alarming facts into a precise instrument for imaging the Earth. Follow the full path from the accessible science to the quantitative frontier.