I am trying to do a project for the Crusades but want to know what are some primary sources I should read. What are the ones that would be considered the most important? Preferably I would like to read some written by both Christian and Muslim authors. Thanks
For the Muslim perspective, the classic is Usamah ibn Munqidh, for which there's a Penguin paperback. It's pretty entertaining at times, but I would caution you that it's a biased source like any other. There's been a tendency among many modern folks to take everything he says at face value.
The best book for getting the Muslim perspective is Carole Hillenbrand, The Crusades: Islamic Perspectives, which is unfortunately out of print. It gives lots of excerpts from primary sources along with Hillenbrand's well-informed narrative.
An older book that anthologizes several Muslim chroniclers is Francesco Gabrieli, ed., Arab Historians of the Crusades. That's also worth reading.
On the Christian side numerous chronicles have been translated and published, some in multiple editions. My personal favorite is probably Robert de Clari, who participated in the Fourth Crusade. He gives more of a sense of what it was like for a rank-and-file participant than most sources do. It's pretty short, too.
If this is a project on the crusades in general, then maybe you want to include something from the First Crusade? Then you could look at Edward Peters, ed., The First Crusade: The Chronicle of Fulcher of Chartres and Other Source Materials. There's also a more recent book from Penguin edited by Christopher Tyerman, Chronicles of the First Crusade. I haven't looked at it but Tyerman's one of the main guys in the field so he probably made good choices.
Regarding sources for the First Crusade u/ghibelline_dream has already recommended some good books but I'd like to add the Gesta Tancredi by Ralph of Caen (translated by Bernard Bacharch and David Bacharch), and Albert of Aachen's History of the Journey to Jerusalem (translated by Susan B. Edgington) as they are both good primary sources from the point of view of the Crusaders. For an eastern Christian view I'd highly recommend the Alexiad by Anne Komnene which you can find an English translation published by Penguin Classics and goes into depth into the First Crusade and its aftermath from the view point of the eastern Roman (Byzantine) Empire. Finally, from a Muslim perspective I'd recommend the work of the Damascene chronicler Ibn Al-Qalanisi, The Damascus Chronicle of the Crusades (translated by H.A.R. Gibb) as it covers the First Crusade and beyond, and the thirteenth-century historian Ibn Al-Athir as part 1 of the English translation of his al-Kamil fi'l-Ta'rikh covers the First Crusade and its aftermath up to the year 1146.
For sources after the First Crusade but covering the twelfth-century I'd recommend the English translation of Walter the Chancellor's The Antiochene Wars as it gives a good history of the Principality of Antioch and its conflicts in the years after the First Crusade. Then there is Otto of Friesing's The Deeds of Frederick Barbarossa which deals with the Second and Third Crusades from the point of view of the German Crusaders, and Odo of Deuil's De Profectione Ludovici VII in Orientem - The Journey of Louis VII To The East which covers the Second Crusade but from the point of view of the French Crusaders And for sources from the eastern Roman point of view there are translations of John Kinnamos' Deeds of John and Manuel Comnenus and the work of Niketas Choniates (translated as O' City of Byzantium, Annals of Niketas Choniates) but these works might be too expensive and if they are a good secondary source that you can use instead is Byzantium and the Crusades by Jonathan Harris as it cover the interactions the eastern Romans had with the Crusades from the First Crusade to the late thirteenth-century. Also another source from an eastern Christian perspective is the Armenian chronicler Matthew of Edessa, whose Chronicle (translated by Ara Edmond Dostourian) covers the period from the late tenth-century to the middle of the twelfth. For Muslim sources besides Ibn Al-Qalanisi and Ibn Al-Athir, which I've already recommended, and Usama Ibn Munqidh, which ghibelline_dream has already recommended, I will instead recommend some secondary sources.
First off there is Taef El-Azhari's Zengi and the Muslim Response to the Crusades: The Politics of Jihad which covers the career of the Turkish general and ruler Zengi as he fought against other Muslim rulers as well as against the Crusaders. Then there is Paul M. Cobb's The Race for Paradise: An Islamic History of the Crusades which does as its subtitle suggests, but its a good overview of the Crusading period in the Levant. And if you want to know more about the Turks in Anatolia during the twelfth-century I'd recommend The Rum Seljuks: Evolution of a Dynasty by Songül Mecit as it gives a good overview of the Seljuks of Rum in the late eleventh and twelfth-centuries and their interactions with the Byzantines, other Muslim states like the Zengids, and the Crusaders using a variety of sources Arabic and Persian sources that are not easily accessible if you do not know the original language or another European language like French or German.
Finally for sources covering Crusades in the thirteenth-century Penguin Classics' Chronicles of the Crusades would be perfect for you as it includes Geoffrey de Villehardouin's The Conquest of Constantinople and covers the Fourth Crusades and the first couple of years of the Latin Empire of Constantinople founded in the wake of the city's sacking, and The Life of Saint Louis by Jean de Joinville which covers the French King Louis IX's participation in the Seventh and Eighth Crusades in 1248 and 1270 respectively. And if you want to learn more about the Crusaders in Greece there is Anne Van Arsdall and Helen Moody's translation of The Old French Chronicle of the Morea: An Account of Frankish Greece after the Fourth Crusade which gives a history of the Principality of the Morea, founded by Crusaders in the aftermath of the Fourth Crusade, and their dealings with their eastern Roman subjects and neighbors. Good luck with you project and I hope I was able to give you something that you start off with.