With the advent of 35mm film cameras came the need to design 35mm lenses. The first still cameras designed to use 35mm film inevitably used lenses modified from use on motion-picture cameras, or microscopes. This made sense when the 35mm cine-film used the 18×24mm frame format, however these lenses only covered part of a 24×36mm frame. The figure below shows frame coverage of a cine (movie) lens versus a 35mm lens.

For instance the Tourist Multiple used a Bausch & Lomb Zeiss 4-element Tessar (50mm f / 3.5 lens), which was used on motion picture cameras.
Leitz, founded in 1869, began as a company focused on the manufacture of microscopes, and other optical instruments. When work began on the Ur-Leica, Barnack and Berek tried a number of lenses. The simplest option was the 5cm f / 3.5 Zeiss Kino-Tessar movie camera lens. The problem is that the lens could not provide a light spot able to cover the 24×36mm frame format, as it was designed for a 18×24mm format. In addition it produced vignetting not suitable for a camera. The lens they ended up using was the 6-element 42mm f / 4.5 Leitz Mikro-Summar, in a classic double-Gauss formula. This lens had a number of shortcomings, including edge blurring, and a lack of contrast.

The design of a new 35mm lens was the responsibility of German physicist and mathematician, Max Berek (1886-1949). The first 35mm lens developed at Leica was a 50mm f/3.5 Anastigmat. Based on the “Cooke Triplet” lens design, it had 5 elements in 3 groups. The lens was later marginally redesigned, still containing 5 elements in 3 groups, and was given the name Elmax (The name is derived from Ernst Leitz and Max Berek.). These lenses were used on the pre-production Leica-0, of which 31 were manufactured from 1920-1925.

At that time, the calculation of such a lens was still very complex. Light beam paths from points near or away from the optical axis had to be calculated for three wavelengths and seven refractive surfaces, all by hand using logarithmic tables. Leitz was granted patent No. 343086 for the Anastigmat in 1920.
The first lens formula was difficult to build, so Berek changed the design to a triplet with the last element a cemented doublet, i.e., 4 elements in 3 groups. This lens was renamed Elmar, and was subsequently manufactured for decades (1925-1961). The lens was similar to a Tessar, except for the location of the diaphragm. On the Elmar the diaphragm was located between the first and second elements, rather than the rear two elements.

The first lenses which appeared were of the fixed type used on the Leica I. From 1930-1959, the Elmar was made in a screw mount, and an M (bayonet) mount from 1954-1961. From 1930-1932 the lenses were matched with one body, after which they became interchangeable (M39 mount). The lens would evolve to have a maximum aperture of f/2.8, and a minimum aperture of f/22. .

Specifications: (Original)
50mm f / 3.5 Elmar lens
Angle of view: 45°
No. of elements: 4
Minimum focusing distance: 1.0m
Minimum aperture: 16
Aperture range: 3.5, 4.5, 6.3, 9, 12.5, 16
Weight: 92g
Here are some links to extra info on early Leica lenses: