Here are some of the more useful books on the First Crusade.  In my opinion, the best introduction is Asbridge, The First Crusade.

Asbridge, Thomas (2004). The First Crusade: A New History. Oxford. ISBN 0-19-517823-8.  [no kindle]

Black, Mark.  The First Crusade: A Very Brief History.

Chazan, Robert (1997). In the Year 1096: The First Crusade and the Jews. Jewish Publication Society. ISBN 0-8276-0575-7. [no kindle]

Christie, N.  (2014). Muslims and Crusaders.  

Edgington, Susan B (2014).  Jerusalem the Golden: The Origins and Impact of the First Crusade.  Brepols.  ISBN-13: 978-2503551722 [no kindle]

Edgington, Susan (2012).  The First Crusade.  

France, John (1997).  Victory in the East: A Military History of the First Crusade.  Cambridge.   ISBN-13: 978-0521589871 [•kindle]

Frankopan, Peter (2012). The First Crusade: The Call from the East. Harvard University Press. ISBN 978-0-674-05994-8. [•kindle]

Harris, Jonathan (2014), Byzantium and the Crusades, Bloomsbury, 2nd ed. ISBN 978-1-78093-767-0.  [•kindle]

Hillenbrand, Carole (2000). The Crusades: Islamic Perspectives. Routledge. ISBN 0-415-92914-8. [no kindle]

Kostick, Conor.  The Siege of Jerusalem: Crusade and Conquest, 1099.  

Nicolle, David (2003). The First Crusade, 1096–99: Conquest of the Holy Land. Osprey Publishing. ISBN 1-84176-515-5. [no kindle] (popular history with nice maps and illustrations)

Rogers, R.  Latin Siege Warfare in the Twelfth Century.  (pages 10-64 analyzes the sieges of the first crusade)

Rubenstein, Jay (2015).  The First Crusade: A Brief History with Documents.  Bedford.  ISBN-13: 978-1457629105.  [no kindle]

Rubenstein, Jay (2011).  Armies of Heaven: The First Crusade and the Quest for Apocalypse.  [•kindle] (focuses on apocalyptic and miraculous elements of the crusader movement)

Runciman, Steven (1987). A History of the Crusades: Volume 1, The First Crusade and the Foundation of the Kingdom of Jerusalem. Cambridge. ISBN 978-0-521-34770-9. [no kindle] (classic narrative history)

Smail, R. (1995). Crusading Warfare: 1097-1193.  2nd ed.  [no kindle] (great source for military issues)