To understand Asmara and Eritrea, three books stand out.
African Titanics by Abu Bakr Khaal (translated from Arabic) is a short, urgent novel that follows would-be migrants from Eritrea across the Sahara toward Europe. It is uncomfortable reading and the best account in fiction of why so many Eritreans leave.
I Didn't Do It For You by Michela Wrong is a smart and sympathetic history of Eritrea from the Italian colonial period to the war with Ethiopia, written by a journalist who knows the country well. The chapters on Asmara during the war are particularly good.
Asmara: Africa's Secret Modernist City by Edward Denison, Guang Yu Ren and Naigzy Gebremedhin is the architectural reference, lavishly photographed and easy to dip into; the perfect companion if you intend to walk the colonial-era circuit seriously.