The first church on the site of the remains of the apostle, James, was built in 829 AD.  This was later destroyed by the Moors.  Construction of the present cathedral began in 1075.  It was built mostly in granite. 
The cathedral, originally Romanesque, was expanded in the Gothic and Baroque styles between the 16th and 18th centuries.   It's twin spires can be seen to the right of the sky line below.

Each of the façades along with their adjoining squares constitute a magnificent urban plaza. The Baroque façade of the Plaza de Obradoiro was completed in 1740. 

 

 

Here is a view of the Plaza de Obradoiro from the cathedral museum, in the body of the cathedral

 

 

 

 

The cloisters are inside the museum

 

 

 

 

Plenty of information can be found at

http://en.wikipedia.org/wiki/Cathedral_of_Santiago_de_Compostela