The hardtop shown above is a Pininfarina top. It is fiberglass with a glass rear window. The rear latches at the front corner of the bottom of the top to the stowed convertible top frame. This is similar to the top that was originally fitted to the Abarth-spec 124 Spiders. Each top has its own serial number plate, found ???.
Above is another Pininfarina hardtop.
The hardtop shown above is an aftermarket one made by "Custom Hardtops" of Long Beach, California. It is fiberglass with ??? rear window and ??? side windows. Inside, it features a ribbed secondary layer of fiberglass for noise- and weather-proofing. Attachment of this top is with ???. A manufacturer's serial number plate is found just above the driver's (left) side front (roll-up) window.
The hardtop shown above is a Snugtop??? hardtop. It is fiberglass with a ??? rear window and ??? side windows. The top appears to be vinyl-covered, but the grain is molded into the actual finish of the top itself. Inside, there is a ribbed plastic liner similar to the Custom Hardtops top. The rear buttresses extend behind the forwardmost trunk line, lengthening the overall appearance of the greenhouse. The rear latches at the ???.

The hardtop shown above was manufactured by Parrish Plastics (which has since become Smoothline Industries) in the Pittsburgh, PA area. The top is a single-layer thick fiberglass with a glued-in felt headliner. The rear attachment of the top is to the Spider's tonneau boot hooks on the rear deck by way of two u-shaped bolts. There is a single wrap-around window made of acrylic/plexiglas. These tops were sold either painted or with a vinyl covering similar to the Landau roofs of 60s/70s American cars. This particular hardtop was painted at the same time as the '68 Spider upon which it is shown for a perfect color match.
Above (to the left) is another Parrish Plastics/Smoothline hardtop, this time shown with the vinyl covering. Unfortunately, the vinyl has seen better days and will need replacement on this particular top. Last time I checked, spare parts were still available from Smoothline. The top shown in the above image on the right side (to the rear of the 850) is another Parrish/Smoothline top, but with fitment for the 850 Spider.
Above is the Parrish Plastics/Smoothline hardtop with black vinyl covering as designed/manufactured for the Fiat 850 Spider.
The hardtop shown above was included with my purchase of our black Lancia Appia vignale Cabriolet, but that is not what it fits. I can tell you that it also does not fit Fiat 850 or Fiat Spider. It looks to have a Pininfarina line to it. It's lightweight metal with steel internal cross-braces for strength. I'd love to know what it's proper fitment is. If you happen to know, please get in touch.