You always hear about the Western European knights and Chivalry, but you hardly hear anything about the Islamic military orginziation and society from these times. Did they even have a warrior class similar to the European knights?
Yes, although the feudal or class-based elements, which exist but are very different in Islamdom, mean that the parallel is imperfect.
The approximate Arabic equivalent term for "chivalry" is furusiyya, which maintains many of the martial qualities of horse-borne warfare, but has fewer of the social connotations. In Europe, courtly or chivalric loves becomes associated with the martial qualities of knights and the nobility. While a similar literary concept exists in the Arabic world in the from of Udhrite love poetry, as far as I'm aware there was no real expectation that it be associated with furusiyya.
As I mentioned, the practice of furusiyya, though it certainly involved a kind of warrior caste status, that caste status could and often did differ markedly from the situation in Europe. In much of the medieval Islamic world, for instance, the military class were technically slaves, as in the example of the Egyptian Mamluks. Nonetheless, whether free or unfree, these horse soldiers very often occupied the same military ruling class positions as their feudal counterparts in Europe.
The forms of land grants and tax farming in the medieval Islamic world varied considerably, and in turn differed significantly from the various forms of European feudalism (leaving aside the entire European medievalist debate about what that was.) As a category, however, medieval Islamic land holding or tax farming rights were part of the "Iqta" system, of which the "military iqta", the granting of land or taxation rights to this military caste in reward for service, was typical.
Where it differed perhaps most markedly from the European nobility is that, at least in theory, the Iqta was entirely at the discretion of the Sultan and was not (necessarily) hereditary, though in practice it could be.
This was also true of the caste as a whole, so for example while Mamluks occupied the highest-status military positions in society, their children, the awlad an-nas, actually could not inherit their fathers' martial status (again, at least in theory. At the margins and over time the institutional clarity of this practice could fluctuate).