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Microwave photonic filters are photonic subsystems designed with the aim of carrying equivalent tasks to those of an ordinary microwave filter within a radio frequency (RF) system or link, bringing supplementary advantages inherent to photonics such as low loss, high bandwidth, immunity to electromagnetic interference (EMI), tunability, and reconfigurability. There is an increasing interest in this subject since, on one hand, emerging broadband wireless access networks and standards spanning from universal mobile telecommunications system (UMTS) to fixed access picocellular networks and including wireless local area network (WLAN), World Interoperability for Microwave Access, Inc. (WIMAX), local multipoint distribution service (LMDS), etc., require an increase in capacity by reducing the coverage area. An enabling technology to obtain this objective is based on radio-over-fiber (RoF) systems where signal processing is carried at a central office to where signals are carried from inexpensive remote antenna units (RAUs). On the other hand, microwave photonic filters can find applications in specialized fields such as radar and photonic beamsteering of phased-arrayed antennas, where dynamical reconfiguration is an added value. This paper provides a tutorial introduction of this subject to the reader not working directly in the field but interested in getting an overall introduction of the subject and also to the researcher wishing to get a comprehensive background before working on the subject.