* Astronomy

Front mounted v Rear mounted filters for small telescopes.

The benefits of a front mounted colour filter system on your telescope are seemingly minor, but important.

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Colour filters can help to bring out planetary, solar and lunar detail. But, all filters, no matter how well manufactured, will introduce aberrations into the light path. For telescopes, especially fast (f6 and lower) telescopes, the main issue, for eyepiece mounted filters, is that the light paths are not parallel; consequently a tiny fraction of the light is reflected between the top and bottom surfaces of the filter - which leads to a loss of contrast and sharpness. This effect can be lessened with quality coatings, and blackening the filter edges; but it still remains as a discernable (mostly photographically) degrading of the image. A front mounted filter effectively negates this particular effect. 
[The front filter will, of course, still be susceptible to front (and rear) surface scatter, reflection, and light absorption within the material, but these particular optical effects can generally* be ignored; and even in low quality filters, are perhaps only just perceptible to the human eye.  Having said that, a good quality antireflection coated, optically flat and planar filter will be better than a low quality filter. It is not uncommon to 'stack' various filters together - with the optical defects compounded and visually apparent.]

Note1: Therefore it is important that any front mounted filter is correctly fitted, flat and at 90 degrees to the light beam.

*It should also be mentioned that the benefits of a correct eyepiece filter for observing usually outbalances the negative effects of any image quality loss.

Test for a Front mounted green filter.

Captured with a 100mm f6 refractor + Vesta pro webcam + solar filter + green filter. ( No other correcting filter used.)

A front mounted filter system also allows for quick and easy filter removal or swapping.

The negative aspect is that the cost of new large sized filters are prohibitively expensive. The good news is that second-hand market prices are comparable, if not cheaper, than eyepiece mounted filters.

The Cokin P Series Filters will fit upto 82mm diameter telescopes.  Larger filter sizes are available but rare. The Cokin system consists of a range of square filters which are held in place in front of the lens by a holder attached to a threaded adapter ring. The main drawback with this system is that the telescopes existing dew shield will not fit, (but a functional one can be fashioned from dark card).

The Cokin Z-Pro range filters measure up to 100 x 150mm.

With a 170mm x 130mm filter size, the Cokin X-PRO series has been created to offer the professional photographer a comprehensive range of filters that can be used on medium and large format camera systems, as well as extreme wide angle lenses used by photographers, videographers and broadcasters.
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Circular screwfit 120mm filters, usually for broadcast video cameras, will have a 100mm clear aperture.

Gelatin filters can be used for very large aperture filter but they are very fragile and have to be replaced periodically, as they are susceptible to fingerprints and water damage. 
Glass has the optical quality but can be heavy and breakable when dropped.
Resin also has good optical qualities and is lightweight and reasonably durable.
Polyester filters are best avoided as they do not have the optically quality.

Note2: While not ideal, an aperture mask can be fitted to large telescopes (for example) for lunar observations; a colour or neutral density filter can then be fitted over the reduced aperture. A stopped down telescope will also improve chromatic aberrations for very fast (short focal ratios) refractors: Aperture masks will also improve contrast in classical Newtonian design reflectors (at the expense of resolution).

Note3: Fresnel equations

For common glass, the reflection coefficient is about 4%. Note that reflection by a window is from the front side as well as the back side, and that some of the light bounces back and forth a number of times between the two sides. The combined reflection coefficient for this case is 2R/(1 + R), when interference can be neglected.
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Note4: Refractive index

In optics the refractive index (or index of refraction) n of a substance (optical medium) is a number that describes how light, or any other radiation, propagates through that medium.
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Ed ~ The bottom line is that for slower (above f8) telescopes there is no noticeable difference between front or rear mounted filters.  For astrophotography with fast telescopes a front mounted system is not essential, but recommended.