The standard contemporary sources (from the Latin side) are Geoffroy de Villehardouin and Robert de Clari (available online at the Internet Medieval Sourcebook). From the Byzantine (contemporary) point of view, there's Niketas Choniates. They're all available in English translation.
Then there's a whole list of smaller sources, e.g. the Historia Constantinopolitana, written by Gunther of Pairis, or the letters to and from Innocent III...
Old French Continuations of William of Tyre (several of them) also cover the subject, though they are in 12/13th Century French so depends on how good you are at translating. Peter Edbury will be publishing them in a couple of years translated.
The Deeds of Pope Innocent III by Anonymous also cover the subject.
Roger of Wendover and Roger of Howden also cover it to a lesser degree
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