Read Keegan's The History of the World War I (title from memory). Austria had to respond to the assassination of the Archduke, just like we had to respond to 9/11. In retrospect, it would have been better if Austria attacked Serbia singlehandedly after Serbia (egged on by the Russians) rejected the ultimatum. But Austria made the mistake of consulting with her allies, which triggered mobilization orders in Russia and Germany, and in turn, in France and England.
Austria is the least blameworthy in the summer of 1914. Its one mistake was hesitance to act singlehandedly, which it was perfectly justified to do.
Serbia agreed to all points of Austria's ultimatum. Austria's Emperor Franz Joseph invaded anyway.
Ultimatum to Serbia
Having received the wholehearted support from Germany, Austria sent an ultimatum to Serbia on July 23, 1914. The ultimatum was to be answered within 48 hours. It included the following demands:
(i) Serbia was to suppress all anti-Austrian (and Pan-Slav) publications, societies and propaganda.
(ii) Serbia was to dismiss all anti-Austrian officials objected by Austria.
(iii) Austrian police and officials were to enter Serbia and to take part in the Serbian police force in order to carry out the suppression of anti-Austrian activities and investigations concerning the Sarajevo murders.
Serbian reply
These demands infringed Serbian sovereignty. Austria expected that Serbia would reject, thus giving her the excuse to declare war. Instead, Serbia accepted the first two demands and suggested the third be submitted for arbitration by the Hague Tribunal. William II was satisfied with the Serbian reply and did not feel the need to punish Serbia with a war. He declared, "a brilliant diplomatic triumph, no excuse for war."
2. Outbreak of War - July 1914
War declared
Austria was still determined to destroy Serbia. After declaring the Serbian reply unsatisfactory, the Austrian government simply declared war anyway on July 28. The bombardment of Belgrade began on July 29.