Earthquake engineering is also illustrated as Seismic engineering. This is one of the most common branches of civil engineering. In this engineering, an engineer can study and learn about the methods to create structures, like buildings & bridges, repellent to the harm incurred by earthquakes.
It basically handles seismic activities and ways to reduce the risk which can happen owing to earthquakes. In the broad sense, earthquake engineering covers the investigation methodologies and various solutions to the problems that could possibly be created by disastrous earthquakes, and consequently, the work involved in the practical application of these solutions, i.e. in planning & designing, constructing and managing earthquake-resistant structures and facilities.
Here is a list of a few books on Earthquake Engineering which is available for free downloading.