Here there is a coverage of the filter types that have been employed for different projects. Digital, analogue, passive, RF, microwave. It is intended as a practical pass through of different design approaches , not a theoretical filter design course. See Tools site for filter designs
The classical LC filters with resistive terminations. Can be used to generate IIR prototypes or active filter prototypes. Nowadays the inherent loss in filters can be circumvented by incorporating op-amps. The toolbox site has a number of passive filter design tools.
The classical digital filters are the FIR (Finite Impulse Response) and IIR (Infinite Imulse Response). Within the FIR clasification we can include interpolation filters.
A sub class of passive filters dedicated to distributed designs. Due to component size becoming the same order of a wavelength at the operating frequency a distributed design approach has to be used, with the complications of harmonic (spurious) pass bands.