Further information and experience has resulted in an update to this post which has been added at the the end.
The FX-3 is as basic as an SLR can be and that is surely one of its attractions. It has all you need to take photographs with nothing extra thrown in. The viewfinder is better than many, the meter is basic, the film advance works and the shutter does its job. And there's a wide range of lenses that can be used with it sold under the Yashica and Zeiss brands.
There's lots of information around the Web describing the FX-3 and there's no point in me repeating the same information here. But, having repaired FX-3s, I probably have a slightly different viewpoint than others.
The FX-3 is built on an almost identical chassis to the Contax 139 and shares some parts with it, particularly in the film advance mechanism and the mirror box assembly. The shutter is, of course, different but, even that, has some similarity to the Contax one and some shared parts. The shutters in both cameras are mechanically (spring) driven but the Contax one is timed electronically while the FX-3 is fully mechanical. Generally, mechanical shutters are not so accurate and this is the case with the FX-3 and, I have found, they can be significantly out if not maintained. But that can happen to electronically timed shutters as well, especially at the higher speeds where the mechanics of the shutter can have a larger effect if not operating correctly.
The shutter is made by Copal and is one of their many variants of the 'square' shutter. The same shutter was used in many entry level SLRs, especially ones built by Cosina as was the FX-3. In common with the FX-3, many of these cameras had an upgrade version released with the top shutter speed raised from 1/1000 to 1/2000 once the shutter was capable of achieving it (for example the Cosina CT-1 becoming the CT-1 Super). Exactly what was changed between the 1/1000 version shutter and the 1/2000 version I don't know as they look identical and the 1/1000 version has a position for the 1/2000 shutter speed though it's not click stopped. The same shutter went on to be developed further to achieve a 1/4000 top speed and was used in the Nikon FM2 and the Contax S2. In my experience, all these variants of the shutter struggle to reach their maximum quoted speed. A review of the FX-3 in a 1980 magazine noted "the top speeds were slow and the slow speeds were fast" which is a clear indication the shutter is struggling at the higher speeds. That said, when working correctly the speeds should be close enough to not cause issues.
One annoying (to me anyway) feature of the FX-3 which it shares with the Contax S2, is the noise it makes. There is a distinctive 'ring' which continues after the shutter has been released. It's caused by some springs in the mirror mechanism that continue to ring after the mirror returns to its normal position. It's an easy fix to damp the springs and give the camera a more positive sound. In the Contax 139, which has the same mechanism, the mirror is damped so the camera doesn't suffer the same problem but, in the FX-3 and also the S2, the mechanical shutter takes up the space where the mirror damper sits in the 139 so it couldn't be fitted.
The FX-3 was initially upgraded in 1984 to become the FX-3 Super (which, confusingly when compared to other upgraded models that used the 'Super' label, did not have the upgraded shutter). The Super variant had a grip added, the meter switch was moved from the back of the camera to the shutter release and an extra contact was added to the hot shoe to enable a flash ready signal to be added to the viewfinder. It wasn't until 1986 that the Super 2000 variant was released with the 1/2000 top shutter speed. The Super 2000 also had a recalibrated meter circuit that shifted the ISO range up by one stop.
The FX-3 is often compared to other similar cameras, especially the Cosina made ones, but often the comparisons are incorrect. Some confusion is caused by the range of budget cameras made by Cosina for other manufacturers which were based on its CT-1 chassis. Although the specifications may be similar, the chassis is different and, in my view, the CT-1 chassis is not as stable - especially the
way the prism/viewfinder is mounted which could cause focus errors. The FX-3 (Contax 139) chassis was used in other cameras made by Cosina, such as the Centon K100 and it seems to have found its way to
some Chinese manufacturers (maybe via Cosina using Chinese factories to assemble cameras) as it appears as a Huaxia DC-1 and a couple of Phenix models and maybe others. Of all these, I would rate the FX-3 as the best, especially considering how cheaply it can be bought these days. Although I also like the Centon K100 which has an electronically controlled shutter (though the one I have has inaccurate shutter speeds).
If you're looking for a user manual for the FX-3 you can download one from that nice Mr Butkus at http://www.cameramanuals.org/yashica_pdf/yashica_fx-3_short.pdf. If you are looking for a service manual, it can be downloaded from my Documents page at the main Contax 139 site.
Update: When writing this post I was under the impression that Cosina had some input on these cameras. My opinion now is Cosina had nothing to do with any Yashica cameras or the many variants made based on the Yashica design. All these cameras were made by Phenix in China.
The shutter used in the Contax S2 and the Nikon FM2n is of the same design as that used in the FX-3 but I couldn't say it's a direct development of the FX-3 shutter. In fact, the FX-3 shutter was further developed to include a top speed of 1/4000 but it wasn't used in the S2. It was used in the Kenko KF-2N and it's clones - the KF-M1 and the DN-66, all made by Phenix.