There are 4 optical versions of this lens:
Nikkor-S 3.5cm 1:2.8 Auto (7 elements, 5 groups) - serial nos 920101 - 9275xx. From early 1960s, difficult to build due to fine tolerances required so is uncommon and soon replaced.
Nikkor-S 35mm 1:2.8 Auto (7 elements, 6 groups) - serial nos 176911 - 392xxx. Common pre-AI version, improved performance and easier to build so was relatively common.
K/Ai 35mm 1:2.8 (6 elements, 6 groups) - serial nos 773111 - 870xxx. Highly regarded version, is sharp with very low geometric distortion, rendition not quite as smooth as older version though.
Ai/AiS 35mm 1:2.8 (5 elements, 5 groups) - serial nos 350001 - 593678. Simpler optical design not as well corrected for geometric distortion, maybe not quite as sharp but with smoother rendition. The Ai version has a very short focus throw, the AiS version is a little better.
5 versions if you include the Series-E 35mm 1:2.5. This has a similar 5 element design as the AiS version, but optimised for more speed and compactness, so the image quality is not at the same level.
7 versions if you include the two PC-Nikkor 35mm 1:2.8 lenses:
Early version with metal focus grip (8 elements, 7 groups) - serial nos 850001 - 886xxx
Upgraded to modern style with rubber focus grip and multicoating, same optics - serial nos 900001 - 909635
Later version (7 elements, 7 groups) - serial nos 179091 - 205761. Styled like AiS lenses, but with manual preset aperture ring is not Auto Indexing (AI). I haven't heard much about how these lenses perform?